If not already mentioned, I found that when my refrigerant was low the system would not engage, not even a little; the light on the switch button will not even go on.
That's basically correct, but our systems have two pressure switches: a low-pressure switch and a high-pressure switch.
If you have far too little refrigerant in the system, the low-pressure switch will register insufficient pressure, and the system won't even start.
If too much pressure builds up, for example, if you have far too much refrigerant in the system, the high-pressure switch will trigger, and the system still won't start.
When you have the right pressure in the system, the low-pressure switch says "go," the high-pressure switch says "go," and the system switches on. The refrigerant is then compressed and flows to the expansion valve until the high-pressure switch registers that the pressure is to high. Then the air conditioning system disengages the magnetic clutch, the pressure is released, and the magnetic clutch re-engages.
If the pressure cannot be released, for example, because you have moisture in the system, the expansion valve is frozen, or the refrigerant isn't being cooled insufficiently because your fans aren't running or your condenser is completely clogged with dirt, this system shutdown will take longer and longer, thus reducing the system's performance.
And if you have just enough refrigerant for the low-pressure switch to signal that the system is ready for operation, the system will start. However, the compressor will then pump refrigerant from the low-pressure to the high-pressure side, causing the pressure in the low-pressure side to drop below the threshold that the low-pressure switch recognizes as the minimum pressure.
In this case, your system would also shut down very fast.
In other words, it's possible that you have just enough refrigerant in the system for it to start, but then shut down shortly after because there isn't enough pressure in the low pressure side.
Therefore, it is extremely important that the refrigerant quantity is exactly right—not too much and not too little—and, above all, that it was filled after a sufficient vacuum was created to remove all moisture from the system.
That's the reason why I'm not really convinced by filling your system DIY. If you have a good experience, a proper vacuum pump, two manometers than this can work.. But those who have good experience, for example because they work in a workshop or have dealt with air conditioning systems their whole life, also have very likely access to an air conditioning service unit.
And incidentally, mistakes are often made in workshops as well. They simply check what amount of refrigerant your vehicle requires and fill the system accordingly. I've seen cases where they did this, but the air conditioning didn't work, and upon closer inspection, the refrigerant level was incorrect because, for example, the vehicle was delivered with different compressors that require different amounts, or different lines were installed, too much oil is in the system, what also can cause to high pressure in the system even with the right quantity of refrigerant, or whatever the reason.
Every air conditioning service unit has pressure gauges that allow you to see the pressure levels on the low-pressure and high-pressure sides while the air conditioning is running. An experienced air conditioning technician can tell from this whether the system contains too much or too little refrigerant. While air conditioning systems are fundamentally simple, they do have their complexities.
Furthermore, it is of course important that the condenser is clear at the front and not completely blocked.
And that the condenser's ventilation, i.e., the cooling system, is functioning. Ideally, this should be done with electric fans.
For older vehicles that still have a viscous coupling, you'll need a bit of airflow while driving.
Hope that helps