Yes, the oil pressure should work as the engine is turning over and building pressure. So, if you have power from the limiter and the the wire to the sending unit isn't broken, then you are left with 3 possibilities; the engine isn't building pressure, the sending unit isnt working, or the gauge isn't working.
I would start by making sure the wire is continuous by using a continuity tester. I would install a manual gauge to ensure the engine is building pressure. If those check out, then you are left with a bad gauge.