A new Main Relay was just installed and the car started. As the problem is/was an intermittent one, only time will tell if a defective main relay was the cause of the problem. Hopefully, this will be my last post on this matter and future viewers of this thread can benefit from the above exchange and the info below.
The old main relay didn't appear to have any broken solder points as others from this forum have observed. I did have someone trained in electronics test the old relay and he assured me that it had a short in it.
This post from Kaspin,
https://www.honda-acura.net/forums/a...p/t-43947.html , instructs on how to perform the repair on an Accord, Civic, and Prelude. Most all steps apply toward working on an '88 Integra with the important exception that the main relay is not easily visible once the fuse panel is removed.
Once you remove the fuse panel you will see several relays attached to a rack (your perspective will be from lying down on the floorboard looking up toward the left side of the car) . The Main Relay (n.b., according to the guy at the parts store, Honda had two different main relays for 1988 models so pull the relay and then give the part number to the supplier) was the last one on the rack (i.e., closest to the firewall) with several yellow, black, and yellow/black wires going into the plug. You have to remove 2 or 3 10mm bolts to detach the rack. Once this is done you can reposition the rack assembly so that a 10mm ratchet wrench can be used to remove the bolt securing the main relay to the rack.
The lowest price I could find from Acura on the part was $62 (online from Delray (Florida) Acura -- good source). I ended up paying the local CarQuest parts store $40 for a new one. The manufacturer of the new one was the same as the original part in the car (Mitsuba, part number RZ-0042 12V).
I was advised to apply White Lithium on the contacts of the main relay. This is recommended if body rust (or any other defect) might allow moisture to reach the main relay.
The start terminals were OK and there were no problems (that were visually obvious) with the clutch switch.
Hope the above helps anyone unfortunate enough to run into this problem.