How do solo fighter pilots sleep?
Generally, the only time fighter pilots are asked to remain airborne long enough where this is a factor are when ferrying aircraft across the ocean, (or for long distances over territory where there are no intermediate refueling bases.)  Generally this is always done in multi-aircraft flights or formations or two or more aircraft, so even in a single seat fighter, you are not completely alone.
Obviously, the average fighter cannot carry fuel sufficient to last that long, so (again, generally), when this happens they accompany a refueling aircraft  (or have pre-planned rendezvous with refueling aircraft every few hours). So there is no need to "wake up" - they remain awake the entire flight. They are flying manually in formation off the wing of the refueling aircraft, or one of the other aircraft in the flight. If the flight is long enough where alertness is an issue, or if the flight occurred during periods where the aircrew would normally have been asleep, we were sometimes issued Dexedrine tablets to take to help remain awake and alert. 

In peacetime, we would never deliberately plan a flight where from start of pre--flight planning, until engine shutdown would exceed 12 hours. This rule of course could be violated in the case of wartime or national emergency, etc. etc.