I just discovered something this evening that you might be interested in, Penguin. The lid switch on an 051 is a red plunger to the top console, microswitch on the circuit board. Even though the lid has a magnet in it (tested with a paperclip, just for fun) and the top console has the mounting point for the reed switch...
If the out-of-balance switch is open-circuit, it seems to turn on but then beep with the spin light on when you try and start. Mine did this until I wiggled the plugs.
I got hold of the 051 for free - it was 'dead'. I opened up the motor controller (totally different to later models - it has water cooling for the transistors!) and found a blown fuse plus evidence of water sitting around the PCB (dry now). I cleaned the circuit board, tested a couple of slightly-scorched resistors (across the largest capacitors), tested a few dodgy-looking PCB tracks (they were fine), and replaced the fuse. Working now
I notice that the connectors seem to suffer more than they do on my newer (and yet more-used) Smartdrive.
I think I would suggest removing the control panel PCB and test with a multimeter where it says '15.5V'. If it's not quite up to voltage, maybe try cleaning the various small plugs on the motor controller board. Maybe keep playing with the power switch until you can get it to 'act up', and then check the voltage?
I'm becoming quite keen on these machines now and suspect I shall have a few more pass through my garage yet