Odd things going on with a Marantz PM500

Ist shot is speaker selector switch depressed and the second is off
 

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So not load current related by the sound of it. I'd have to look at the circuit and have a think on that one.

If the amp turns on OK with the EQ switch already pressed in then I would next see it it is all basically functional in that state. In other words DC offset correct and that it sounds 'normal'. Just don't operate the switch with speakers connected.

Ist shot is speaker selector switch depressed and the second is off

If you are measuring that at the speaker terminals then it looks normal, the output is floating when the speakers are off and will be picking up loads of stray hum and noise.
 
Can you clarify exactly what trips?

Is this a user resettable trip on or in the amp itself (like a button) or do you mean something else like a trip external to the amp (in the home like a leakage breaker).

If it is in the amp can you locate it on the circuit diagram so we can see exactly what this trip is.
 
That looks like the speaker relay and it will be being tripped by a sudden shift in the DC voltage at the amp output.

You will need to look at the EQ circuitry (identify the EQ switch on the circuit) and see what the EQ switch actually does. There should be no change in DC conditions when the switch is operated. It sounds like the power amp input/s are seeing a sudden step change in DC voltage and that is triggering the DC offset protection.