If I recall correctly, ground for the starter relay circuit is made inside the switch by a small tab of metal that contacts the handlebar. Of the 3 wires, one is hot power to the switch, one becomes hot to the coils when the switch is slid to ON, the third is the wire that gives the ground from the bar to the starter relay. If you want to check my work, (I haven't been "vetted" on this forum yet), check for continuity from the 3 wire pigtail to one of the terminals on the relay. It's an easy find, your schematic will give you the terminal number. My 850 LeMans did the same thing, took the switch apart and right where the little tab was given a surface to make contact with bare metal, there was some rust preventing it. The slightest rotation of the switch would take away the bare metal spot to contact. Switch will pull apart laterally, as Steve K. says, BE CAREFULL. Miniature springs, tiny pieces, nothing really robust. If that is what is going on, due to cleanable detritus, or that the little metal tab has lost some of it's spring, maybe you can tweek it a bit to give it more tension against the bar.
TdF