1941 Commander 8 - Overdrive

You have what is known as an (~)R6, if I recall. These operate quite a bit differently than the later units. On these, the upshift is controlled by internal mechanical flyweights.
As long as the lockout lever on the side of the overdrive is pushed to the rear, the overdrive should become available about 30 mph or so. Take your foot off the gas and it should upshift.
It will downshift at say 15 or so. All of this is without any electrical equipment, so you can test the transmission by merely driving after moving the lockout lever to the rear.
The solenoid on the side of the unit only provides kickdown when the one terminal that does not test as open is provided with power. The other terminal, which should show as open, provides a momentary ground for the point side of the ignition coil.
This causes the engine to skip a beat and allows the downshift to be accomplished. Sometime in the near future I will get my 41 out of the barn and can post some photos if you still need them.

If you push that lever next to the embossed "R7" to the rear and then go for a drive, you might well find out that you have a functional overdrive. Might want to wire the lever back for the test. Get the car up to 30 or so, release your foot quickly off the gas and in a second or two you will feel the car drop into overdrive. It will drop back out at a very low speed provided there is no torque being transmitted. Before this test, make sure your idle speed is moderate, about 500 max, or that will inhibit the upshift.

As mentioned, with this overdrive there is no need for the electrical controls to work. They only provide kickdown. Please report back with your findings and then we can tackle the electrics.