Thanks for the responses.
I am using a rev3 Mega 2560, it claims to be genuine. Though I recently modified it by replacing the linear regulator IC1 with a switch mode 5v 5a regulator - I removed the reg and ran wires to the pads.
The mod appears to have solved the problem, except for a little weirdness when adding or removing the usb or external 12v. I think it rebooted when I touched usb ground the board ground before plugging it in, which could be problematic in future.
I couldn’t actually run the board with only the 12v supply before modifying it. The various leds would flash on and then die, only to turn on again but nothing else happened. I suspected it was boot looping or the little linear regulator was cutting off to stop itself cooking.
The micro and lcd would run fine with only USB power, but that’s not much use because I need the 12v to run motors and such.
It is good to know that I can remove the 5v from the usb without losing communication though, that will be useful.
Edit. Alas I do not own a scope.