Dave:
I just went through the same thing. Fan clutch locks into high speed with dash A/C compressor function so both were short cycling. In my case, dash air was cooling just fine but with the cycling every few seconds, something won’t last long. Took to local shop. Big mistake. Spec for the 134a refrigerant for my 2000 chasis is 6# 10oz. They evacuated the system and recovered 6# and so said low on freon and replaced up to the 6/10. That killed the cooling from the dash and now there was an additional cycling with the high pressure switch kicking on and off at 320 psi – as it is supposed to. Had them let off freon until that stopped.
Then I checked ohms of the fan clutch. Spec for high side (A to C) is 35-42 ohms. I got 8. Put in new fan clutch and problem went away.
I have seen cars short cycle when low on freon but usually associated with bad cooling. I never lost cooling.
That was my experience. Mike
2000 Featherlite H3-45
2024 Jeep Grand Cherokee
Leesburg, FL