I saw a pattern on this site for 2001's and the compressor cycling frequently. My refrigerant charge was low, I think they shorted the R134A on the 2001 tracs.
I bought a gauge kit and filled it some. No more constant clicking.
While I had the gauge connected, it would drop to the low side of the filled pressure, then the compressor would engage, and the pressure would rise to the warning area, then the compressor would disengage and the pressure would drop. This cycle was repeated with 10 - 20 seconds between "clicks".
I did a few things:
Found a loose vaccum hose under glove box in the passenger side footwell. A white rigid tube with a blue silicone elbow, attached to a black device. This was causing the pressure in the AC system to rise drastically and anytime I went over 2000RPM the cooling would stop. re-attaching the line stopped that issue.
Added a r134A / oil blend until the clicks stopped, and the pressure stabilized in the blue "filled" area on the gauge.
Increased my idle speed by turning in the idle adjust screw. Someone wrote a really nice idle adjust project on this site, look for it. My Trac idles between 750 and 850 RPM in park with no accessories running, and doesn't drop below 650 in drive, with the radio, headlamps, wipers, and AC on full blast.