Congrats on the find!
Lots of stuff decays over 30 years and your issues are rather common.
Headlight: The headlight power actually passes through the starter switch, so the headlight will go off when using electric start. This switch disintegrates inside after a few decades, and I would look there first. Just bypassing the headlight cutoff works fine, the starter works about the same with headlight on anyway.
Wiring in general - if you have the owner's booklet, there should be a fold-out wiring diagram in it. If you don't have this, GET THE REAL HONDA WIRING DIAGRAM!!! This can be downloaded from various places, but these images can be of dubious quality. I can copy and send you one if necessary - whatever you do, don't rely on ANY other wiring diagram: they are all inaccurate.
"sopo400f" has the right advice - clean all the electrical connectors throughout the harness. Some are in the headlight bucket, a lot are under the fuel tank near the steering tube on the left side, some under the side covers, and a few important ones under the left engine cover. If you find some badly burnt bullet connectors (you probably will) you can try cleaning the metal parts but they should be replaced.
That done, you should find the electrical gremlins gone. If not, they will be easy to trace with no mysterious faults from bad connections.
Your carbs need a good cleaning. I would also replace the float valves and gaskets, but these parts cost about $200.00 all together from Honda. You can get "carb kits" from Sirius and elsewhere with OK gaskets but the jets should not be used unless yours are damaged, even then you should buy Keihin jets and toss the aftermarket ones in my opinion.
The float valves can be cleaned and "rejuvenated" if the needles have brass tips, if they have black rubber tips, leaking = trash.
Possibly the dripping overflows (which means leaking float valves) come from dirty gas - little bits of rust or dirt stick in the float valve. Some members here deride inline fuel filters and even blame them for fuel starvation problems but I have used them for 40 years without a problem. And my carbs have been getting clean fuel - float leaks are rare with filtered fuel.
Brake bleeding - always a problem. I've found that reverse bleeding gets the bubbles out of the brakeswitch tee best. I loosen the caliper and pump the piston out quite a ways (adding fuel to the reservoir as required). Then using a C-clamp on the caliper I force the fluid back up to the MC while keeping a rag over the reservoir to avoid spraying brake fluid over the paintwork. The bubbles want to float, so pumping them down towards the caliper is counterproductive. This way they get flushed out of the crevices in the tee and out the MC. This is basically pressure bleeding, used on most ABS brake systems. If you can get a pressure bleeding kit that's good, but you have to grease up the bleeder nipple threads so the fluid doesn't seep past as much.
Maybe I'll see you in Owen Sound some day. Keep riding!
