A PA28 pilot landed without clearance because he was distracted troubleshooting a right main landing gear light not illuminated. On short final; the light finally illuminated.

Narrative

On approach to the runway I was instructed to report 2 mile final. At approximately 4 mile final I selected gear down and witnessed nose and left main gear light illuminated but no right main. At this point before my landing check is complete and I am ready for landing. I played with the light to see if perhaps the bulb was out. At this point approximately 1 mile has passed. Moments away from deciding to go around and try and troubleshoot the landing gear; the right landing gear indicator light illuminated indicating down and locked. So I checked and double checked the light to make sure that it was in fact illuminated. Now no more than 2.5 miles from touchdown nerves shaken and adrenalin pumping that I may have just had my first emergency I am confident that the gear is down and locked. Well in the aftermath of dealing with the landing gear situation and everything going ten times faster when you feel like that; I forgot to make my 2 mile final position report and continued my approach to landing and landed without a landing clearance. There is almost no acceptable excuse for landing without a clearance and I completely accept full responsibility for the fact that I let the situation get ahead of me and continued without clearance. I never realized what I had done until upon taxi I was instructed to call tower. There are many things I could have done differently and better ways I could have handled it; after all hindsight is always 20/20 but I was mostly glad that the gear was locked upon touchdown and that there was no major accident.