My manual is for a 93 so I am not sure but it should be the same on wiring. There are three wires going into the trans switch. The yellow one is for neutral safety provision. The 18 gage WT is power to backup lights. The 18 gage VT/ BK is power out to backup lights. I think the VT/BK means violet with a black stripe. Put the trans in reverse with the engine off > ingnition key on. (Make sure to block the wheels to keep it from rolling). Then probe the violet wire to see if you have power on it. If you do go to the back of the truck and check the plug where the wires split off to the lights. It might be corrided up or damaged.
The PCM (power train control Module) controls >Heater relay #1, generator fields, heater relay #2, ignition feed, ASD relay (auto shutdown relay) , MIL (malfunction light on dash), Tach (which I don't think yours was wired for from the factory), vehicle speed sensor, ECT sensor ( I have no idea), water in fuel sensor, Air intake sensor, CKP pickup (crank position sensor), thermo switch (trans high temp switch) plus other items.
The items you have listed as bypassed doesn't mean that the computer is bad. There are sensors in each circuit that can go bad and stop the computer from sending the right signal for them to function.
Do you have a factory service manual?
Your truck is a 91. 5 model if it has the a OD trans in it. The early 91's only had the 727 3 spd auto. So on your sig for the truck. List it as a 91. 5. This will tell us that it is the later model config.