Some serious information is likely to be required here. Seems like there are two generic possibilities: too little charge or too much demand. Since it charges 8 amps with no load and negative with the cutter solenoid energized, the solenoid must be consuming more than 8 amps, or the charge rate is decreased for some reason when the solenoid is turned on.
1. What is the specified current draw of the solenoid?
2. Is there any switching arrangement that changes the alternator output when the solenoid is turned on?
To clarify what I am getting at here, I used to have a Honda step-through bike with an alternator direct-driven on the end of the crankshaft. It just turned out a couple of amps more than the ignition system required normally, but when you switched on the lights, some extra alternator poles came on line and output went up to 4 amps. Now if some amateur messed with the wiring, so current output went down instead of up when you switched on the lights ...
