I think a weak battery could do that on a four-cylinder GL - Especially if you’re running electronic ignition. I know for a fact that the behavior you describe exactly happens when the Valkyrie has a weak battery.
'97 Valkyrie, '86 VMax, '79 CBX-Z, '78 GL1000, '83 Voyager Lite Project, '78 750F BIG Project, '74 750K HUGE Project
"Motorcycling is not, of itself, inherently dangerous. It is, however, extremely unforgiving of inattention, ignorance, incompetence or stupidity." - Anonymous