Use Ohms law to get to the current by measuring the voltage over the resistor instead.

Great idea! I should've known that myself!
/me hits myself repeatedly in the forehead
I now found out something even more interesting: the voltage on the majestic remote-turn-on lead actually goes to 11.5V immediately if I take the empeg out. It goes back to slowly increase, if I put it in and stays 0 if I ground the 1kOhm wire. All the time, the ignition is off and the empeg, therefore, is also off. The turn-on wire is not connected to either the empeg, nor the other amp. Thus, the only connection between the empeg and the majestic amp are the RCA cables. What does it mean that the voltage disappears, if the empeg is plugged into the sled, vs. it being out of the sled? The majestic amp is grounded to chassis with a very short wire (about 5 inches, 10-15cm). The "front" and "rear" RCAs go into a splitter at the Memphis amp and one end of the "Y" goes into that amp and the other into the majestic amp. I find that all very confusing...