Maybe that is the problem (Strainer clogged)
But everything you stated that your gage is doing is exactly what mine was doing. It didn't do it in the summer. always when it's cold. always at start up. bounce up and down a couple of times and then be ok and alright for the rest of the day until the next morning when it was completely cold.

My truck is an 01' and only has 41K on it. When I removed the sending unit it had oil in where the wire plugs in. It has been a problem on these trucks.
I would change the sending unit first and then if it still does it then you've got big problems.
If you had no oil pressure to the top of the motor you would hear it in the engine.
Do you have any laboring sounds like clicking,clattering or squealing?
If not and the engine sounds good you need a oil sending unit.