I currently own a '96 Goldwing 1500 SE and previously to that I owned a '91 Goldwing 1500. Both bikes have the same exact problem. If they sit for 3-5 week period, they won't start. I found that when I take the fuel line off the gas filter there's no gas coming out while cranking. But when I leave off the key it gives a small squirt. Then, I have to take the bike apart to get to the carb. I give 1 small squirt of carb cleaner and then the bike start instantly. It runs perfect as long as the bike is used weekly. I was told by a retired Honda mechanic that there was a recall on some sort of module for that year. However, I haven't been able to find any info regarding the recall or this problem. Any help would be appreciated.
I think if I were going at it, I would check the fuel pump first. If you download the GL1500 Service Manual from the "Manuals" page here, have a look at page 4-40 for the procedure. That will at least rule it out as the source of the problem.