AC works by compressing the refrigerant then letting it expand back to "normal" pressure which causes the cooling effect
There are two pressure switches in the system, high pressure switch which will be located after the compressor, and low pressure switch which will be located after the expansion.
These switches are closed when system is working correctly.
High pressure switch keeps lines/seams from blowing out
Low pressure switch prevents compressor from running dry, running out of refrigerant to compress
On older models the compressor's 12volt activation voltage ran from AC ON switch thru each pressure switch and then to compressor, so if either switch was open compressor would shut off(no AC)
Later models used the Ground for compressor voltage, but same result, if either pressure switch opened then no AC
Your 1999 uses the Ground thru the pressure switches but........it goes to the Engine Computer(PCM)
The AC on switch goes to PCM, PCM then passes the pressure switch Ground to the AC compressor Relay in the engine fuse box
When AC relay closes 12volts is sent to the Compressor
Ground--------pressure switch-----------pressure switch-----------computer------AC relay
Reason computer(PCM) was added to the AC system is so it can shut off the compressor at WOT(wide open throttle), and if engine should start to over heat.
I would test if switches are closed key off, use OHM meter
Then start engine and run AC until it shuts off on its own, then turn off engine and retest switches to see if one is now OPEN
Could be the AC relay is going bad, long shot, but if both pressure switches are closed and AC won't come on then that would be next stop