PA-18 general aviation pilot reported an engine failure while entering the traffic pattern for landing due to fuel exhaustion in one of the two tanks. The pilot glided the aircraft to a safe landing; then the engine restarted and the pilot taxied to parking.

Narrative

The flight was a return cross country from ZZZ1 to ZZZ with a stop at ZZZ2 for fuel. The fuel stop added additional time to the already long 3:30 flight in the dark. The PA-18 has only a L and R fuel selector. There was no clock on the instrument panel (basic panel) but I did have my EFB . After ZZZ2 airport; a 30min alarm was set on my EFB for switching tanks. The estimated fuel burn was calculated to be approximately 18gal from ZZZ2; with full tanks (18gal per side; 36gal total). As the flight progressed; the controllers became harder to hear due to going farther from the terminal radar areas enroute along a highway. This resulted in having to use the squelch function on the radio and adding another distraction and fatigue point to the flight. The route of flight later split from the highway then straight over to ZZZ via a valley. This was difficult to navigate as there were no clear landing areas and constant searching of cars on roads was used to find the safest route. This resulted in additional distractions and fatigue. At some point due to the additional distractions; the EFB timer was acknowledged but never reset. This was not my plane and did not have the same systems as I am used to with my personal plane. My personal plane has a engine Instrument System or EIS that has an internal timer for every 30min to switch tanks. This gives a red blinking ENGINE light as a reminder. The PA-18 did not have this system. On descent to ZZZ; a final climb was made from the valley to clear the last mountain range with ample altitude at 11;500ft. After the airport was in gliding distance; a high speed descent was made to the airport arriving on downwind about 1000ft above pattern altitude. At midfield; the engine abruptly stopped. I pulled carb heat; went full rich; and slowed to best glide speed. I [advised ATC] and landed with no issues dead stick on RWY XXL. The engine came back to life and taxied to parking with no issues. Upon return the right fuel tank was found to be empty with 3/4 fuel remaining on the left tank.During the engine out it did not occur to me that fuel exhaustion was a possible issue. Having been more worried about navigation; engine health (monitoring CHTs and oil temp and pressure). The fuel gauges are also overhead and slightly behind the front seat. These are unlighted and required a flashlight to check them. The plane progressively became more out of trim in roll but did not connect the dots that it was due to a fuel imbalance.Finally; there was no emergency checklist in the plane. A standard checklist was created for all normal phases of flight and was available to use. However; the cruise checklist was not thorough enough and did not prompt periodic checks.Lastly; this was at the end of the day after a 3.25hr flight to ZZZ1 from ZZZ.