The best way to test the solenoid after a run where the OD did not engage is take the solenoid off and shake it. It should rattle with sharp clicks. If muffled, there is fluid inside.

If you do not want to take it off, get a long piece of wire and connect one end to the positive battery terminal. Crawl under the drivers side and remove the yellow wire from the solenoid. Leave the ground attached. Touch the test wire to the terminal. The solenoid should click, very sharp and crisp. Removing power should also yield a click as the slug is pushed back. It will not be very loud as the spring is not all that strong but it should be crisp.

Do this after the OD has not disengaged. The longer the time lag the less definitive this test becomes.

A yellow wire carries power from inside the vehicle to the solenoid. IF a relay system (push button on shifter)there is a red wire that connects the relay to ground through the 4th gear switch. If the red is always grounded, the dash light would stay on when you shifted out of 4th. If the yellow wire was grounded, you'd blow a fuse when going into OD which you are not so no wire to ground problem.

If a slide switch, the power routes through the 4th gear switch to the solenoid and a ground in the wire would blow the fuse when you engage OD, again no way from your description since you have OD, just cannot get rid of it at times.

Not sure but I think the reverse light wires are blue with yellow stripe as power and black to the lights under the auto. The switch is on the top left of the gearbox cover.

Duane