I agree that the pulse generators could be the cause.Mine would stall for no reason when I was riding and sometimes I could even get it started before I coasted to a stop.It was very intermittent sometimes every few miles or hundreds other times..
I decided to replace the pulse generators just to eliminate them and found that the problem was comming from a broken wire right at the top generator it was so close that I wasn't able to repair it properly. Seems that every once in a while the wire would loose contact and cause a failure.Have had no more problems since they were replaced Dave
On the 86 Wings, the "PG's" are located behind the cam-belt cover on the front of the engine. The "parts" are harder to find than they are to replace. You may want to get a manual and do some further trouble-shooting. The Pulse Coils/generators are a known weak spot for the 1200 series. But with a 23 year old bike electrical connections,coils and plug wires could also be suspect. You might even try carrying a spare plug with you, and the next time it stalls you could swap it out to verify spark, or the lack there of. Just one more step before digging into the wallet...
And welcome to the forum, the folks here are friendly and all about helping...:gunhead:
im had that problem all summer until i change the pulse generatos working great now mind was doing excactly what yours is doing sometime it would go for 100 milles and some time a few hundred feet sometimes it would start right up and other times i had to let it cool down a few minutes