E30 Zone

The touring I bought was sold as having oil pressure issues. The light is on as soon as you turn the engine on. But it doesn't sounds as bad as other m40's I've had.

I don't currently have a oil pressure testing kit. Was just looking at some cheap ones on ebay and amazon. Am I right in thinking its a m12 thread? Are these cheap (£25) kits ok?

I've had a quick skim through the search function and other possibles could be, faulty wiring or the sensor itself, right?

M12 x 1,5 thread.

Is the light on all the time the ignition is on or the engine is running? Is it dependant on the temperature of the engine?
If the single wire shorts to earth (unlikely on a M40) the light will turn on, and it's not particularly unusual for a pressure switch to start switching at a higher pressure than it should.