Ford didn't put a 5.8 into any 1997 F150s.....
Short cycling compressor clutch is a sure sign of a low charge. That means you have a leak in the system that should be repaired before recharging.
The stock clutch plate can separate and cause a very loud click when engaging/disengaging, often accompanied by a rattling while disengaged. The outer clutch hub is available from Ford for around $50-60. you can look up the correct part number at www.motorcraft.com
For a 97 with a 5.4 (at least), the correct replacement is YB-3020. Do NOT purchase the after market POS from AutoZone.