BE36 pilot reported the engine failed on short final approach and during landing a flap struck a runway light.

Narrative

While landing in the BE36 I did not see three green landing gear down and locked indicators after landing gear down extension. I aborted the landing. I was taught that gear problems are not an emergency and that one should get the POH Pilot Operating Handbook out and follow the documented procedures to resolve the problem. I exited the tower airspace to work the problem. I circled outside of the towered airspace for approximately 35 minutes during this time. Returning to land I was cleared to land behind another aircraft. I expected the aircraft I was following to make a normal runway landing and exit onto the taxiway but they took the full length of the runway to exit at the far end. I slowed from 80 kts to 75 kts to give increased spacing. On the close approach I was startled to have loss of engine power. I enriched the mixture; engaged the boost pump; and switched fuel tanks. The engine did not catch immediately and before power developed I realized I needed to focus on making the best landing possible without power. On landing the runway approach side red/green end light was struck by the fully extended left flap. I should have switched tanks first and then enriched the mixture and engaged the boost pump. I should have maintained more flight energy to be able to make a power off glide to the runway. I was distracted by absence of three green gear down lock indicators; which was caused by having the Nav lights on which dims the gear lights.