MPV Starter won't start on Hot engine

Our 1991 Mazda MPV. Won't crank on hot engine, I hear clicking sound. I have to pause for few minutes and turn on & off the headlights. Battery is new and original starter had been cleaned & brush checked. Start fine on cold or warm engine.

oil leaking from rear engine pass. side from pvc port and blanking plate o-ring seals can penetrate solenoid which becomes inoperative with hot engine
This was my problem some time ago which I fixed by cleaning solenoid and replacing the o ring seals also if this is your problem replace the lower heater hose which also can be weakened by this oil leak