Perhaps it's poor grounding to the Empeg as opposed to something drawing excessive current?
During the fault condition a bad ground could float above
real chassis ground. Since (from the Empeg's perspective) it's supply voltage is the difference between the +12v feed & it's ground connection this
could be a cause.
If you have a Voltmeter you can test this by measuring between *real* chassis and the *actual* Empeg ground connection while the fault condition exists. If you get a reading above (e.g.) 0.5v then this could be the cause.
Alternatively you could just skip the voltmeter part and run temporarily a big fat cable across the bonnet (or the
hood if you have one of those instead

) straight to the chassis earth near the battery for testing purposes.