I can't answer the questions you are asking. But do want to mention I had the same problem with my 2001 Bonneville A/C clutch not engaging. I checked the fuses and relays. All good.
I then read a post that low freon can prevent the clutch from engaing. I purchased a freon fill canister with attached gauge. It reported empty. I filled the system with freon, and my A/C clutch started to work and has worked fine for the past 45 days.