I thought I understood the solution last night after reading the first two responses, but one response this morning has only confused me again, as it seems to contradict the other two responses...

Muzza says "try running a lead directly between the battery and the empeg always on power " and tfabris says "do make sure to run the player from a line that's run straight from the battery... This might solve the problem."

But Schofiel says "the ignition switched 12V ...is the main power feed to the Mk 2:". Wouldn't this mean that the switched 12v lead is the crucial one (the one that needs a more stable voltage supply), not the unswitched one?