Psi oil gauge moving a lot, is that normal?

I would have the oil pressure checked with a manual gauge first, some gauge swing is normal for electronic gauges but yours sounds excessive.

I'd expect pressure at idle to be around 30 psi, when accelerating, around 60, and at highway speed about 40. So yours seems close to that and on a car that age, it's pretty normal. You might have a mechanic analyze that. With the ranges you have you could have something going out, like cam/crank bearings or oil pressure resistor or switch. Or maybe the car has high miles and it needs a rebuild.

The oil pump is driven by the engine. So when you accelerate the oil pump speeds up too and pumps more oil so the pressure goes up. Oil pressure will also be higher when the engine is cold because the oil is thicker. Hope that helps! Jim