Re: maybe all related
If you have a test meter, watch your battery voltage with the motor off vs the motor running. Ideally it will be 12+ volts motor off and a little higher (13+) while running. If you see the voltage drop below 12 while operating the trim, you may have an alternator problem. If the voltage at the battery does not change, you could just have connection problems. I agree it "sounds electrical" but I certainly don't know enough about the entire system to say for sure.
Good Luck,
Andy