The only place I've had any luck finding discontinued parts is here...
https://www.cmsnl.com/honda-motorcycles_model2/
and you find the part, put it on your watchlist and they notify you when they have found one.
Might want to look at this seat? Thinking it's not a 1200, maybe a 1100. Course it might be exactly what you have....
https://goldwingdocs.com/forum/viewtopic.php?f=9&t=72631&sid=73abcfc2dc36e3032ec9056d012d16f2
The easiest place to look for driveline slop is the rear wheel. Remove wheel and check the gears for excessive wear and the pins that connect wheel to drive.
This is shown on 14-9 and 14-10 of the FSM
https://classicgoldwings.com/media/wheels-and-tires-14-09.31210/...
If it was me, I would replace both while I was in there. My luck would be the other one fails right after it's all put back together.
I may not have been clear on the ohm test, the measurement would be done without the part being in the bike (ie the sensor not sensing anything metal).
Look at this wiring diagram....
https://classicgoldwings.com/media/page-142.19766/
It shows the color of wires and based on what you state the 'blue' doesn't sound right. You need to measure ohms on the pairs to see if they are good or bad. I don't remember the resistance (ohms) it should...