[sambo]

It actually happens without the engine running - turn the key from OFF to ACC then OFF again.

I've had a breakthrough. I removed one fuse at a time and tried the key each time to see whether I could isolate the problem circuit. Turns out when I remove the fuse for the pos feed to the amp (open circuit) the starter problem goes away. The earth to the amp has 0 ohms resistance (good) so it must be the positive that has a bad contact. I've used a heavy gauge wire with really chunky strands so I'll try a thinner wire and see what happens.