12v trigger ground loop

I'm getting a ground loop hum when the 12v trigger wire is connected between the preamp and power amp. I have ruled out everything source wise and tried an earth ground between the two components without success. If I remove the ground connection completely from the trigger wire gets rid of the hum and the trigger still works. I know running without a ground is not great solution if something should ever go wrong in the trigger circuits of either the preamp or amp.

Putting a 480ohm resister in series with the ground should still allow the circuit to complete but break the ground loop. Question is, is this better/worse than no ground at all?
 

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Ohm's law isn't relevant, you just need to have much more resistance than the part of the ground loop that's injecting voltage into the amp, which is typically a piece of copper wire.
Think resistive divider, with the trigger ground being the top resistor...