A real conundrum!

I have a 1987 Izusu PUP which goes dead in the heat and leaves me stranded. It does this only on hot days and does not seem to have any pattern as to whether or not I drive a fair piece or only to the store. It also has no pattern as to how long I let it sit after parking. When I go to start it the door buzzer will sound but there is no reaction whatsoever to turning the key. It is just like a dead battery but when I let it sit it will start again anywhere from 15 minutes to 3 hours. I try an park on hills and jump start it (manual transmition) which usually works but sometimes this will not work either. When this happens it is as though the truck is not getting any gas. Also, I have used a jump from other motorists which works 95% of the time but this has failed me also. There just is no rythme or reason to the problem. Of course the mechanics tell me to have it towed when this happens but by the time the vehicle gets there it will start. Help meeeeeeeee!

Hot day in January? One cause of the problem could be a worn shaft bushing in your distributor. Your mechanic needs to turn the engine enough to line up one of the vanes on the distributor shaft with the ignitor. then put a feeler gauge between the vane and the ignitor that just fits, usually 0.010" then push the shaft away from the ignitor with his finger. If it opens up more that 0.007", its worn out.

Does it CRANK but not start, or does it do NOTHING, no click, no crank, nothing…

prime suspects are poor connections between battery, chassis, and starter.

Does this have a voltage gauge or is the battery light coming on at all while you’re driving?

I don’t remember the exact specifics, but the charging/starting wiring is screwy on older Isuzu trucks. One issue is that some of them are wired such that they won’t run if the alternator goes out and an intermittent alternator can cause screwy problems like you describe.

I would definitely lean more in favor of a bad battery connection or ground connection (IIRC on the Troopers the chassis ground was often troublesome), but if that all checks out you might look at the alternator.

no crank no nothing