My 2012 Prius V with 172,000 miles started having the oil light comes on even when the oil is full?

I would not drive it anywhere.

There are a couple possibilities;

1. Actual low oil pressure with several potential causes but all severely damaging to the engine

or

2. Something is wrong with the oil pressure switch which is relatively inexpensive to fix and would not be damaging to the engine.

 

Are you seeing the light on all the time, or a lot, like easy to catch it that way? Or just blinking on now and then?

If easy to catch, like on all the time, you could try pulling the wire connector right off the oil pressure switch, and secure it so it isn't touching any metal, and let the engine start up, and see if the warning light is still on. If it's on even when the wire isn't connected to the pressure switch, you've likely just got a wiring problem.

If you have an ohmmeter, you could use that for confirmation, just clipping it between the oil switch terminal and grounded metal. It should show continuity when the engine is stopped. You want it to show no-continuity pretty much right away after the engine starts up. If that's what you see, then you could be pretty sure the right engine oil things are happening, and a wiring issue is the thing to track down.