My carrier furnace ignitor clicks and ignites the pilot and continues clicking for up to about 15 min when the main burner finally lights, and then the unit works fine until it tries to relight again. I am thinking I should replace the 3-wire pilot burner. Am I on the right track? The part is # LH680005 at furnaceparts.com thanks

Most likely the problem. My last service call this evening was for just that problem, replaced pilot and house is toasty again. In the short term, rap on the pilot switch a few times with the handle end of a screwdriver. Sometimes this will improve response...

It's a good chance the pilot assembly is bad. A dirty pilot orifice or pilot hood will give the same symptom. A good cleaning may help and save a few hundred bucks.