The shutter circuit appears quite simple on a Polaroid 450. I'm not an electronics engineer, but I know enough to understand that a photocell provides varying resistance depending on the amount of light that reaches it. If we can find out the resistance to shutter speed ratio, we can control the shutter speed by simply bypassing the electric eye and feeding the shutter circuit the resistance necessary for a particular shutter speed.

I realize that others have developed digital shutter control for these cameras, but it requires either purchasing a circuit board and other parts, or buying the components yourself, assembling the circuit and programming the chip, etc. Plus, when I checked the program used to fire the shutter, I didn't like how the shutter worked: it energizes the shutter solenoid when you cock the shutter and stays energized until you take the photo. And you need to completely rewire the shutter circuit, gutting pretty much everything in place and replacing it with the digital circuit.

So here's a method that an average person can do with basic soldering skills. The most difficult part is removing the electric eye and soldering wires in its place. It's also a little tricky if you want to retain the option of an automatic shutter, which will involve bending a contact on the electric eye, soldering a lead to it, and replacing the electric eye.

Research

First, I came up with a shutter to resistance ratio with both the open and closed aperture settings. This is the "indoors" (open) vs "sunny day only" (closed) setting indicated above the lens:

This table gives you 2 ways to build the array: one where each value is built by combining resistors, and the other where each accumulated value is the sum of all the ones before it. You'll notice the math doesn't add up. This is due to resistor tolerance. When building an array using accumulated values, you should build it on the fly, otherwise the accumulated value go off from the official resistor values. The advantage of building the array with accumulated values is that all the resistors fit under the 12 point switch, whereas the individual values stretch out to one side making the array quite a bit bigger.

Notice the values above 1/8 second are pretty much linear in their ratio. Below that, it departs from a linear relationship. I've tested this on the original model 100 and the model 450 and the values are the same.

Wiring a pack camera for manual shutter control

Diassemble the shutter body. This will involve 3 screws and removing the aluminum sticker indicating the aperture setting. Unscrew the shutter circuit from the back of the body. You may need to cock the shutter to get at one screw. Desolder the electric eye from the circuit board. The plastic covering on top will likely melt a bit so do this as quickly as possible.
If you don't want an automatic exposure option, solder some leads to the electric eye terminals, then jump down to Making the resistor array
If you want to retain automatic exposure as an option, look at this wiring diagram to see how this circuit will eventually be wired. A switch will be used to choose between auto and manual exposure.
Bend one of the terminals of the electric eye 90 degrees so it doesn't get soldered to the circuit board again, and attach a lead to it.
Make a cut in the plastic that the electric eye sits in to make room for the 90 degree wire, then insert the electric eye into the circuit board and solder the unbent terminal and one of the leads to the circuit board, and another lead to the empty terminal on the circuit board. You should have 3 wires coming from the shutter circuit.

Making the resistor array

Using the above table, solder the accumulated value for each resistor(s) in series, connecting one switch terminal to the next in a cascading manner. Start with a 470 ohm resistor, soldering it to terminal 12, leaving the other end of the resistor free to solder to the lead to the electric eye. The accumulated value will be the sum of all the resistors in series, depending on the position of the switch. Because of this, you just need to solder the leads from the electric eye to the middle terminal and the resistor soldered to the 1/1000 sec terminal of the rotary switch.
If you would rather build the array with individual values for each switch point, solder the appropriate resistors to each terminal of a 12 point single pole switch. You'll likely need to combine values to reach the necessary value.
Cover each line with heat shrink tubing to prevent any shorts. This was the way I did my first 2 manual conversions, but having done an array in series, I would recommend that method.
Fold the resistors 90 degrees and solder all the leads together. This will connect to one of the leads which goes to the electric eye terminal. Connect the other lead from the other electric eye terminal to the middle terminal on the sliding switch. Then, connect the lead from the electric eye on one end of the switch and the resistor array to the other. This will allow you to switch back and forth between manual and automatic shutter.
I would test the array before putting everything back together. Test the 1/2 second and compare it to a known good shutter. If it is slow or fast, you can adjust it by moving the trim POT on the side of the shutter circuit. The POT at the top of the camera seems to fine adjust the timing. Counterclockwise makes the shutter slower, and clockwise makes it faster.

You have two choices in going forward: You can use a plug in resistor array dongle (which can be used for multiple cameras), or you can hard wire the resistor array into the camera.

Installing a 2.5mm jack to use with a resistor array dongle

Use this method if you want manual shutter control to be an add-on to the camera. One resistor array can be used with multiple cameras. The camera operates in automatic exposure mode by default. When you plug in the resistor array, the camera uses that for manual shutter control. The array "dongle" slides into the flash mount. Files for the dongle can be downloaded here

Cut the plastic shroud at the top of the circuit wide enough for a 2.5mm jack. Line up the lens body with the circuit board and mark where the 2.5mm jack hole should be drilled, then drill a hole for the jack.
Solder the leads coming from the circuit board to the 2.5mm jack: The lead coming from the electric eye gets soldered to the switch terminal, the lead from the circuit board that the electric eye did not get soldered to gets soldered to the tip terminal (which is a closed circuit with the prior lead when no jack is inserted), and the lead from the circuit board that the electric is IS soldered to gets soldered to the barrel lead (usually on the side of the jack).
Install the jack into the drilled hole and assemble the lens body. Before screwing everything together, verify that automatic exposure works without a jack plugged in. Then, plug in a 2.5mm plug and verify that the shutter is on bulb mode (shutter stays open as long as you press the shutter).
Print up the resistor array box and mount found here. 400 series files are for 400 series cameras. Install the array into the box and glue on the bottom, feeding the leads out the edge hole.
Here's the finished dongle attached to a 400 series camera.

Hard wiring the cable to the battery compartment

This method can be used for a one off installation of the resistor array. If this is the only camera you are going to be installing the array into, or if you want to ensure you'll always have the capabilities of manual shutter control with your camera, this is a good method. Two holes will need to be drilled into the camera back/body: one for the array knob, and the other for the auto/manual switch.

Run the wire along the battery cable to the battery compartment.
Pull the wires to the top of the battery compartment. You'll have 3 leads: two for the electric eye, and the other to switch between using the electric eye or the resistor array.
I mounted the rotary switch on the side of the camera which allows it to stay in place when opening the battery door. Drill a hole and insert the rotary switch shaft.
Make a shutter speed indicator and mount it, then screw the swtich in. This particular manual shutter speed control gives the camera shutter speeds in 1/2 steps under 1/60, for shooting paper negatives. A 12 point switch should give you 1/1000 sec to 1 sec and bulb for a normal camera.
Here's the finished paper negative camera. I scribbled an aperture scale reminding me of the apertures on the different settings and ASA speeds. When the aperture is in the closed position, I need to decrease the shutter speed by 2 stops. Under 1/4 second I have to look up the shutter speed on a table. Here's a table with aperture values vs ASA/open/closed settings:
Model 350, 360, 440, 450, 455 ASA open closed 75 f/8.8 f/17.5 150 f/12.5 f/25 300 f/17.5 f/35 3000 f/8.8 f/60
When using the closed settings, the shutter speed is 2 stops slower, so for instance, 1/125 with the open setting will be 1/30 with the closed setting.
Model 100, 230, 240, 250 ASA open closed 75 f/8.8 f/17.5 150 f/8.8 f/25 300 f/12.5 f/35 3000 f/8.8 f/45
The closed setting will shoot 2 stops slower like with the model 350/450. Additionally, with the open setting, ASA 150 and 300 will shoot 1 stop faster than the shutter speed indicated. Best to avoid those settings and just use f/8.8 with ASA 75, then use the closed settings with an additional 2 stops.
I made labels that can be printed, laminated, then trimmed to size and glued onto the lens body to remind you what aperture you're working with. There are 3 labels: one for models 100, 230, 240, and 250, one for models 340 and 350, and another for models 360, 440, 450, and 455. You can get them here
Here's a finished hardwired camera with speeds from bulb to 1/1000 sec.

Feel free to contact me with any questions or news about your build!