1990 LA 360 stops running when hot (help please)

Replace the ballast resistor first followed by the ECU box.

Most likely is the ballast resistor has failed and has a crack in the windings on the primary start circuit that becomes seperated with heat. However, the ECU could have a similar issue.

It’s cheap to just replace both and will likely fix it for little cost. 30 year old electronic parts are probably due to get replaced anyway.
A 1990 Maxi Van will have a TBI and PCM... no ballast or ECU. I would start with the distributor pickup coil. Gets hot, pickup fails... It's a longshot, but if a local shop/dealer has an old pre-OBD scanner and remembers how to use it, it may help narrow it down a bit for you.