1995 GMC Safari VIN W Code 83

I have been chasing codes and repairing the components that would trigger a code.
The only code (other that 12) left is... Problem: Code 83 - TCC PWN Solenoid Circuit Fault
Rough idle in neutral, almost dies when put into gear. Excessive vibration
There is no terminal F wire present at the ALDL so I couldn’t check for voltage there.
I checked the fuse for "Gages" and I see voltage across both terminals with a DMM.
I checked the tan/black wire at the 20 pin connector at the passenger side of the transmission and there was no voltage with the key in the on position. There is supposed to be lettered markings on the male or female end of the plug but I couldn’t see any indication of letters molded into either side of the plug. I also cleaned the plug with contact cleaner.
I went to check for 12 volts across the brake switch which is described in a TCC test procedure. The procedure references one of two possible brake switches, an upper switch with a vacuum hose and two wires, or, according to the document, there is a lower switch with four wires. The document is ambiguous as to whether one or both of these systems are present on the van.
As I am poking around trying to find these components, (which I still have to find) I put my hand on a solenoid that actuates a plunger that has a cable attached to the end and two wires attached to the solenoid, which is attached to the steering column. The solenoid gets so hot when the key is "ON" that I could not leave my finger on the solenoid for a half of one second before it burned my finger! It is located on the steering column and actuates when the brake pedal is depressed a small amount.
I am sure that this is a problem because any solenoid that gets that hot has a problem. I do not know the name of this component to get a replacement, so...
Question #1 - What is the name of this component so I can tell the parts store the correct name for them to look it up on their computer database?
Question #2 - What brake connections do I need to check for voltage beyond the one listed above. I initially could not find a typical brake switch which would be a plunger with two wires connected and attached to the brake pedal directly. I can see where the typical mounts for this type of switch would be located, but nothing is in the mount.
Question #3 – Are there other circuits that need to be tested in the TCC circuits.
I have asked this question on other forums, with no responses. I hope that one of the readers of this post can assist me.
Thanks, James
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