Well, if this random diagram I found on line is correct, (it claims to be a 2002 LS V8 diagram) it could indicate a problem the *relay* for the A/C clutch, rather than the clutch directly. I'd replace that relay first. (or swap it with a less important, identical one.)
it also looks like that fuse controls a couple other things. perhaps the problem lies with a different system. of the three things listed, the solenoid should be the largest electrical load. I wouldn't have the slightest clue where to find it though.