Try wiring a 1kOhm, or so, resistor between the amp remote terminal and ground.
Might bleed off the buildup...

I put the resistor in there and it does bleed the buildup nicely. However, I measure quite some current going through the resistor. Problem is, while my multimeter works just fine for resistance and voltage, it gives me weird readings for current! If I set it to 10A it reads 0.57. If I set it to 2000mA it says 57, if I set it to 20mA it says 5.7???? That doesn"t make any sense to me at all. There is a big difference between 570mA and 5.7. The multimeter works just dandy in all other aspects, but that just throws me off. How much current is actually going throug the resistor "down the drain"? According to Ohm's law (I=U/R=12V/1000ohm) I shouldn't get more than 12mA, so should I assume it's only 5.7mA (which would be perfect)?