Re: 1989 Cherokee Headlights Not Working (flashing on and off)
It's a LONG time ago that I worked on cars, but as I recall, self-resetting circuit breakers were common for headlights. The theory was that if the circuit began to draw sufficient current to pose a threat to the wiring, the breaker would open the circuit to prevent that. But after the breaker cooled off a bit (they were all thermally actuated in those days) it would close again, enabling the lights. No manual resetting.
This kind of thing would be cyclical - that is, the repetitions would be of about the same duration. So I would ask you if the timing of the on-off cycles seems to be repetitive. (A loose connection or some such would tend to be erratic and vibration sensitive. You don't mention anything like that in your description.)
If they are, and there's no wiring problem, the cause may be the breaker itself. Circuit breakers, like fuses, can fatigue with use over time, and therefore can trip (or blow) with no actual circuit malfunction.
Thus, if your mechanic can't define a specific cause, I'd suggest you locate and replace the circuit breaker for the headlights.