When driving air cuts in and out. what causes this
air conditioner cutting in and out on 2003 Cadillac DeVille
A faulty electrical connection anywhere in the a/c system could be causing your problem. If you can have a qualified technician look over your a/c system when it is NOT working it should not be to difficult to pinpoint the cause of your problem. Trying to diagnose the system when it IS working could prove quite difficult and cause everyone a lot of hardship. That being said, there may be fault codes stored in your a/c control module that could help isolate the cause of your problem.
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I would say that it could be that you are low on freon R-134, the newer model vehicles when low on refrigerant tends to click of and on. In the older model cars you had the sight glass that showed you the bubbles indicating that you needed to add more R-134 to the system.