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.
If your original owner's manual is missing, download a soft copy from www.fleet.ford.com
under the MAINTENANCE tab.
1989 Taurus SHO What a project! Retired at 249K.
1997 Ford F150 SC 5.4L - Gone
1995 Mustang GT Convertible, only 68K miles.
1998 Ford Contour Wifey's old daily driver, now mine.
2001 F250 SD, 6.8L, 4 X4.
2007 Mercury Mariner AWD - Wifey's new daily driver