Yup you have it there is a pressure switch that only enables the clutch if there is enough gas, you can buy cans of sealant/oil and gas for 30 bucks.
Auto A/C typically needs to maintain a low side pressure of 40 psi minimum to overide the low pressure switch Chris mentioned. As long as you haven’t had too much dirty air enter the system a small can should bring your pressure up to snuff.If not you will need to run an evacuation ( vacumn pump required) to purge all the dirty air to make it work. Most recharge cans these days have leak check dye in them that will show up a persistent leak( Uses a blacklight to check Hippy). Happy fixing.
Everything Rich said.
Don’t screw around with leaks either. Test for leaks properly yourself or get a shop you know and trust to do a complete and proper pressure/leak test, and replace ANYTHING that’s leaking, even a little bit. (Fully depressurize the system before replacing anything, too!)
Low-pressure switches are standard in an A/C system. The purpose is to cut off the compressor which will burn out if it’s engaged without a proper amount of coolant and coolant-oil (suspended in the coolant/oil mixture as it flows through the system.) Use an inexpensive part to protect an expensive part; just like fuses.
I have a 4 digit repair bill to my A/C system from a few years ago that taught me this lesson.
I also learned a lesson about an unethical (non-local) shop that tried to charge my A/C system and then claimed it wasn’t continuing to work due to a faulty pressure switch that they needed my consent to bypass. I didn’t know any better at the time and gave my consent, just wanting to get back on the road with a working A/C system which seemed to work well so I continued on my way. The next day the A/C was back to non-operational.
By the time I got it in for service with what is now my trusted local mechanics shop, the compressor had seized, adding considerably to my final repair bill.
The unethical non-local repair shop has been avoided like the plague as a result.