I made up a schematic of the Onan 6500 genset control board and although I didn't record wire colors, I can give you what the functions of mine were:
1 - Dash Remote CTR terminal (goes to CenTeR of the MOM switch on dash. When plugged into the genset board, measure ground here).
2 - Dash Remote switch terminal STOP
3 - Dash Remote switch terminal START
4 - Empty or spare
5 - Empty or spare
6 - Dash Generator Lamp (Lights when generator is running).
You can easily pry out the Generator start switch and check wire colors there.
Note that on the board, pin 1 is ground so with the main 12 pin connector plugged in, you should measure at the 6-pin connector on the board and it'll show low resistance to ground. Also, those connectors have a obvious flat spot indicating pin 1.
Looks to me like that loose wire would go between the brown and red wire, there would be 2 empty holes, than the blue wire.
My blog has a generator thread, that 6-pin you've got the disconnected wire on is the one where corrosion had open circuited pin 3 on the PCB so the genset wouldn't start from the dash switch. I added a jumper from pin 3 to 4 on the PCB and moved the start wire down one position.
Genset repairs...