Join Date: Nov 2015
Location: Victoria BC Canada
Model: 1985 GL1200 Limited Edition and 1995 GL1500 SE CDN Edition
Have an '85 LTD fuel injected model, just one year older than yours. These bikes are practically the same.
Do you have the manuals and such, if not PM me and I can send digital copies. This will get you started.
You are correct in that finding someone or a shop to work on your bike will be a quest unto itself. The best thing is to get the manuals and start from there. I did this exact same thing 19 months ago when I bought my '85 LTD.
To start I'd recommend getting a multimeter and start to check for voltage.
Take your battery to a battery shop and have it load tested to eliminate it from the equation. Next I would make sure power is flowing through the starter solenoid correctly.
There is a red wire, red/white striped wire, yellow/red striped wire and a green/red striped wire. The attached drawing explains how the wiring of the starter solenoid is connected. On the LTD and SE-i there is a second white wire from the battery terminal going to the main relay and has a 30 amp in line fuse. Check this as well.
The red wire goes out to the ignition switch.
The red/white striped wire is from the rectifier/regulator and charges the battery.
The yellow/red striped wire from the start switch and the green/red striped ground wire is used to energize the internal starter relay coil. When this coil is energized, power flows to the starter. You haven't mentioned this yet, but I'm guessing the bike turns over.
If the bike is turning over, there is power getting to the ignition switch and out to the bike electrical system.
To check the engine stop switch (kill switch) you can test the black/white striped wire connected to the coils. You remove the seat and the false tank/shelter. Locate the coils in the forward end of the bike. Locate the black/white striped wire connected to the right coil (easiest to work with). with the key on there should be power to this wire, if there is the engine stop switch is working properly.
Let me chew on this to give some additional information on the electrics. Too much at one time is not always the best.
Give the above a try and let us know how things are progressing.
"When writing the story of your life, Don't let anyone else hold the pen"