from the schematic it looks like there's 12v direct to the light, and the sidestand switch provides the ground when its down. Then when you put it up the ground path is broken for the light, and another ground path is created for a wire from the ECU. If that ECU wire ground is broken, then it won't start. So what it sounds like is you're providing the ground to the ECU well enough, but there's something amiss in the switch or wiring that continues to ground the wire from the indicator bulb regardless of sidestand position. check the switch and wires for clues. The wire from the bulb is the yellow/black one, the ground wire is the green one, and the ECU wire is green/white.
I don't see anything in the schematic that indicates the rectifier would be involved, that's more related to the neutral light.