An interesting problem this one...
In particular, I find it interesting that both cars in this thread are 86 cars.
The interesting thing about 86 cars, is they were sold with an interesting airflow meter and ECU package which were just for 86... The ECU change was just that 86 cars had a socketed chip for maps (85 had several socketed chips) in 87 the chip changed for a larger capacity one which held the maps and the software... More interesting was the airflow meter change.
In 87, BOSCH changed the design of the airflow meter slightly, partly due to unusually running problems, due to oxide forming betwen the wiper and the sprung loaded pickup which transmitted the signal level from the wiper to the socket.
So it could be that your suffering from this problem.. in which case, the addition of a wire to the AFM wiper assembly could solve the problem.
Other possible causes could be...
water contamination of your fuel tank... I have seen this before where the car will run fine if run daily, or after the first run following storage for a few days... addition of a fuel system stabiliser to your fuel often cures this. Often the real cause is a poorly sealing fuel filler cap, allowing rain water to enter the tank via the cap seal and capillary action.
Head gasket failure in minor levels can also do this.. where a small amount of coolant enters the bore while stored for a few days... which when run, fouls a plug or two... then when stopped, evaporates off due to the hot engine... if run again after an hour or two, there isnt coolant in the bore, the plug is no longer fouled, but if left for a few days the problem returns.... but in these cases the car also suffers from a mysterious coolant loss problem (often quite minor, but its there)
The last problem I have seen like this was due to a slightly leaky water pump, leaking at the pulley seal... again like the head gasket issue, leaks a little coolant into the belt cover when stored for a few days... once the engine is started, this coolant is whipped up into the distributor cap, causing all kinds of issues.. but once the engine bay warms up a bit, the coolant evaporates, and the problem goes away, unless the coolant has a chance to collect again, which takes a few days.. But again, this often is married with a coolant loss issue.
My money would be on the airflow meter though.