I have a high efficiency Rheem gas forced air furnace. Occasionally, after the induction fan runs for a bit, the main blower kicks on, runs for a minute or two blowing cold air, kicks off for a minute, then kicks on again and blows hot air. Whenever this happens, I also hear a clunking noise right before the main blower kicks on for the first time. I happened to be able to watch the furnace one time when this happened, and I noticed that at the time the burner normally ignites, instead of lighting, there appears to be a significant amount of pressure in the furnace, to the point of bowing the cover plate out (hence, the clunking noise of sheet metal bending).

I explained this to the service technician who was doing the annual maintenance on the furnace, and he said he couldn't identify the issue and that the furnace was in good shape.

Any ideas on what is causing the non-lighting / pressure in the furnace?

Sounds really strange to me. Did the servicer perform any combustion analysis? If not, I suggest you contact another service company who can & will do such.