It does sound like you are low on refrigerant if the compressor is cycling that fast.
Your description seems to be off a little. Compressor should come on at 40 ps1 (aprox) and cycle off at aprox 28-30. The formula I use for high side is ambient temp x2= lower high side psi and plus 50 for the highest psi. (Ex 80*x2= 160 minimum, 210 maximum) YMMV.
High humidity will raise those numbers,as will weak air flow across the condenser.

Curly

 

You could bypass the low pressure switch to get the pump to stay on untill you get the pressure up, what happens is with the compressor on in pulls the pressure down and the switch kills the compresor, I use a saftey pin with the head cut off, cross it out.....or just keep adding 134 till the comp stays on 2 8 oz cans should be enough......never mind the off pressure unless it's high
(over 50psi) remember to check your filter or offrius tube shoulda put a new one before you charged it (only 3 or 4 bucks)

curly is right, but sometimes if a system is completly down it takes awhile for
the refridgerant to get where it needs to be, plus with your comp cycling on and off it's finkle especialy in hot weather.your gauge might not be what the sensor is seeing......that's why i cross mine out. Just trying to help.....

 

From the TJ FSM.

If Low side pressure is low and the high side pressure is low -

1. Low refrigerant
2. Refrigerant flow through the accumulator restricted
3. Refrigerant flow through the evaporator restricted
4. Faulty compressor

 

 

High side pressures are more important than low side. With your 75 degrees the high side should be 2.0-2.2 x ambient temp..........150-165 and the low side should be cold back to the compressor.

 

Ok just as I thought, so it is low I presume that the low side requirements ftgiles posted up should hold true thus the compressor is on. I think im going to short it add until it reaches requirements then remove short

 

Here's the whole page from the TJ Factory Service Manual. Step #6 says just that. If you want the trouble shooting charts, they following on the next three pages in the FSM. I could post them too if you want them. But, it looks like you just don't have enough refrigerant so far, based on your numbers.

 

Thanks ftgiles for the information. It was exactly what I was looking for.