Oil warning light - odd circumstances.

[Offgrid]

Now that I'm on the home straight with the ignition and exhaust, I'm turning my attention to the routine maintenance stuff. First, a bit of background. The car is a 1990 745 with a B200E engine. I bought it over a year ago, and it's been on a SORN for that period. I've only driven it for about 5 miles, but I have run up the engine intermittently. Over the last few days, I've idled the engine for an hour or two each day. This is to clear the engine, and look for any problems prior to its MOT. It idles at about 600 rpm, and I'll adjust that when I've replaced the ignition leads etc. I think the previous owner had started to prepare it for an MOT, but gave up to turn his attention to the restoration of a Morris Minor. It looks as if it has a new air filter, and new very clean oil at the max level. However, the oil filter looks as if it has been repainted. For the last couple of days, the oil warning light has been coming on, and only goes out if I take the revs over 1,200. There is a new oil filter still in its box the came with the car.
What could be causing the warning, and what should I do about it? Obviously, I can't change the filter without changing the oil. The only causes I can think of are - blocked oil ways, a blocked filter, or a failed oil pump. My possible solutions are -

- Run the warm engine at 3,000 revs every day for about 5 minutes.
- Change the oil and the filter.
- Although the vehicle is now insured, I can't run it on the road without a valid MOT.
- Fit an oil pressure gauge, and check the reading at various rev ranges.
- Fit a new oil pump.

What would you do?