1998 Gc A/c

I have a 1998 Jeep Grand Cherokee with A/C not working. I bought a recharging kit but the pressure on the low side fluctuates from about 20 psi to 45 psi. The compressor cycles on and off every 3 second or so. Is that normal? I didn't want to add any R134a as the pressure seems Ok when the compressor is on.

Is there a leak? blockage? should I add refrigerant any way? If there is a problem with the High side how do I check that pressure?

Help please!!!!

I just went thru this on my 95 gc. I used a two part stop leak kit (I had a diagnosed evaporator leak), then one big can of 134a. Cooling wasn't great and I found I had the same condition you did (quick cycling and pressure closer to 25#). Adding another smaller can of 134a got the pressure up to 45# and the compressor running constantly, not cycling. Things have been working just right for several weeks now. I've never had to touch the high pressure side in my shade tree a/c work... even with a compressor replacement and vacuuming the system. All the potential problems you cite are possible, but if it seems the problem is that bad, I'd let a pro look at it. Hope this helps.

Seems to me from what I have read that what you are describing is a low presssure situation, or a bad pressure/cycle switch.
You can temporarily bypass the switch by unplugging the connector from the top of the evaporator and jumping the terminals with a wire. If the clutch engages, and it runs and starts getting cold, then you probably have enough freon (since it's getting cold) and your switch is bad. If it never gets cold even with the switch jumped, then the switch is probably OK and you are low on freon. The service manual says that this is a valid way to keep the compressor running while adding freon to the system if your pressure is so low at the start that the clutch won't cycle on.
However, the best way to check pressure in the system is always with a gauge of some sort.