Thanks Andy, it's not that the on/off switch is special; it's just a conventional microswitch, with the NO terminal cut off.
It seems to work differently on the LED versions, as opposed to the LCD ones though, which is why I posed the question.
On the LED one, it only charges with the switch "off" i.e. to the left.
This depresses the microswitch's NC contact, and seems to disconnect the measuring electronics/display, but allows charging. It's a 4.8v cell stack, and the micrometer can be used with a flat battery with the PSU, provided it's turned on of course, but the battery won't re-charge when the device is in use.
The LCD one only seems to charge its 3.6v battery with the switch on as far as I can tell, but the battery discharges even when the micrometer is switched off.
There is a warning in the LED manual, and also on the end of a different LCD model to mine, that the device should never be powered up without a battery fitted, as it can lead to the electronics being damaged.
My LCD one was demonstrated as working OK on ebay by being shown plugged in, but without a battery fitted, so I'm trying to suss out if it's caused a problem. (The battery, end cap and battery contacts were all missing, but I knew that when I bought it)
The LED one uses a 5v supply and the LCD one a 9v wall wart, but since they are old tech, the off-load voltage is a lot higher in both cases, which I guess is what might cause damage.
For the 9v one I've replaced it with a PSU from an old BT home hub, which is regulated (switch mode??) and supplies a stable 9v, regardless of load.
Also, yes, I'm guessing that the "C" button is for a serial digital output, as there is a 6 way connector as the charging port, though I only have a 2 pin plug for it.
This is part of the reason I'm trying to track down a manual.
My LED ones are M&W, the LCD is branded CADAR, but has a DigitalMicrometersltd sticker as well.
Cheers for the assistance
Bill