Your best plan of attack is to find and purchase or somehow acquire a service manual. It will be money and/or time well spent. The electrical gurus here man be able to help but even with a service manual right in front of you, you will have to give detailed questions and info as well as be very patient. Many here have full-time jobs so can only help as best can do.
As hogcowboy suggested, an official service manual is really going to help you. The Clymer one is alright, but it covers many of the XL's and not so much the 80s...also the 85 service manual doesnt cover alot of the 1980 version. The one you need is here:
Search ebay: HONDA-FACTORY-SERVICE-MANUAL-XL75-77-79-XL80S-80-84
As the xl80s is a 6v system, its pretty simple. It could be something as simple as the ground wire being frayed off on the block next to the stator. There could also be some corrosion behind the stator...get you a puller here:
HIAORS 24mm 27mm Magneto Remove Flywheel Puller Repair Tool for GY6 50 125 150CC 157QMJ Honda Yamaha Suzuki KTM Scooter Coolster 150 Quad ATV SSR 125cc Dirt Bike
Check the points and such, clean it all up.
Now back by the battery there are only 2 components a turn signal relay/blinker and a rectifier. Ive attached some photos from the manual, I hope this helps. I ended up changing mine to a 12v system (kinda expensive) but Im doing a full restore...