Is it Alternate Air?

Or low vac?

I suspect what you are looking at is a circular red "light" just to the left of the gear handle. (You might want to post a picture so we don't have to guess.) If so, there should be a placard that says "GR SAFETY BY PASS" there. This is the landing gear safety circuit (squat switch) indicator and bypass button. (This is something that should have been explained to you by your CFI during your checkout in the airplane.)

Normally you cannot retract the gear on the ground, but by pressing this button, you bypass the safety circuit and the gear may be retracted under any conditions. Normally you would use this only when testing the gear on the ground when the plane is on jacks. Any other attempt to retract the gear when it isn't safe to do so causes a light behind this button to flash and the gear to remain where it is. The flashing red light has two purposes: to tell you that you are trying to do something stupid and also to point you to where you can override the airplane and continue on your present course to do something stupid. (Ok, not stupid if you are on jacks during the annual inspection, but any other time ...)

The fact that it is flashing during normal operation says that there is something wrong with the wiring and/or indicator components of the landing gear. The aircraft "thinks" it is unsafe and you are trying to retract the gear on the ground which is not the case. This means you should take the plane to your A&P and have the gear position switches, squat switch, and landing gear indicator wiring inspected. What you are hoping for is that it fails on the ground with the light flashing with the gear-lever in the "down" position. Having the fault condition occur on the ground makes it easy to troubleshoot. Otherwise you will have to identify all the possible sources for that erroneous indication and start isolating them one-by-one, followed by flight testing. This can add many hours and many dollars to the process.

Regardless, this could be a precursor to a more general failure of the landing gear control circuitry which could potentially lead to the gear accidentally retracting on the ground (VERY expensive) or being unable to retract or extend the gear in flight (just annoying but could possibly strand you somewhere very inconvenient).

So, it is time to make friends with your local A&P. Welcome to the joy of airplane ownership!

I haven't worked on a J-model since they were almost new (late 70's) but if I could see a schematic for this bird I'd be able to help.  It doesn't make sense that it would be a squat switch bypass for maintenance (as CFII surmises above), as when an aircraft is on jacks the squat switch is in flight mode.  However, if it is hooked to an airspeed switch, the above explanation makes perfect sense.

Enjoy your "201"!  Wonderful aircraft

Consider moving the conversation to the forum section for better traction. Best regards, -a-

CFI is correct, but pic is always helpful when trying to troubleshoot.