Oil Pressure Light When Ignition Off

Hi Guys,
Wondered if anyone might be able to help me with this one?
I am just in the process of getting our Coupe back on the road, after being on a SORN for the last five years.
I have just completed preparatory work on all the advisories from the last MOT, so that will hopefully get through the next one with no issues. But while completing this work, I have noticed that the oil pressure light glows when I reconnect the battery. It goes out when I run the engine and the pressure goes up to 3 bar, only dropping very slightly (if any) when I rev it. Then when I turn the ignition off, the warning light comes back on after a short time.
I have checked the wiring and everything seems fine, so at a loss to what might be wrong. Any ideas and advice would be much appreciated. Thanks.

From past experience when that light is on it's shows the alternator is faulty/failing, it's back feeding which brings on the low oil light.

Hi thanks for your comment.
Do you think that it might 'clear' when I've had the chance to take the car out for a decent run? I'm thinking that having a car covered up in storage isn't ideal and problems can materialise.

I've never known them get better, rebuild or replace will probably be the outcome of this as it's common with coupés that have been stored for years and not started on a regular basis.

Thanks for your help. I'll probably replace it when I've got the car MOT'd.

Keep an eye on your battery voltage, alternator might not be charging fully.