OK, so we know the oil pressure doesn't depend on the electric circuits, but the oil pressure
gauge does. So the gauge may be in error for reasons yet unknown.
We also know that the oil pressure depends solely on the mechanics of the engine, and will drop if the engine RPM drops or dies, or drop if the bearing clearances become excessive, etc. But otherwise,
if the oil pressure wasn't a problem before, it's not a problem now. The
gauge's performance may have changed for some reason.
As for the engine hesitation, it's time to investigate.
Are there any codes set?
@someotherguy's remarks are noteworthy too.