I had the same exact problem on my 2000 LeSabre. Lots of clicking going on under the seat when pushing the heater button, but the indicator light would stay on HI. Turning the key off was the only way to reset it off.
It was out of GM warranty but still under an extended warranty. They replaced the heater element in the seat which solved the problem. I think it was about a $1000.00 job.
FYI, checkout
formatting link
for tsb 01-08-50-012a Nov 02, interior - front heated seat inoperative. I don't know if this helps since I don't have access to the full description.Good luck!!!