Gsxrpig,
Can you be specific about which control sets you are using? Are they the ones from your donor 1992 GSX-R 750?
You are correct in saying that eliminating the BMU will not have any effect upon your flasher problem.
A Japanese flasher circuit is quite simple. A source of power connects to one side of the flasher, powering it. The output on the second pin will be a source of regular 12V pulses that goes to the wiper of the indicator switch, a single pole double throw centre off switch. The purpose of the switch is to route these regular pulses either to parallel connected lights on the left side or right side of the bike, depending on which side of the switch is selected. The rapid flashing indicates too little electrical load, meaning you've introduced a wiring error.
Can you post a schematic on how you connected your indicator circuit? If it were me, I would
1. connect the Blue/Red and Blue/Black wires from the old flasher to the indicator switch in the left hand controls
2. connect the Green/Black wire from the old flasher to the new 2-pin flasher
3. run a new wire from the 2-pin flasher to the indicator switch in the left hand controls