1998 Honda Civic Car stalls--replaced PGM/FI relay, still h

I'm attempting to repair my wife's 1998 Civic LX. It recently started stalling once in a while. It has no previous history of stalling. I removed the PGM/FI relay and inspected it; there was a bad solder joint. Since the relay was old and it does contain wearing parts (the contacts), I replaced it with a brand-new OEM relay. This seemed to cure the problem for a day. Unfortunately, the car stalled again this evening. I noticed this time that the dash briefly went dark just before it stalled and I heard relays "clicking, " which leads me to believe:

1.) The problem is electrical and
2.) It's not the fuel pump (if it were, the dash wouldn't go dark).

The battery clamps are tight, all fuses and relays seem to be seated (both under the hood and beneath the dash). It crossed my mind that this could be the ignition switch failing, but that also wouldn't explain the momentary dash darkness--the dash illumination is independent of the state of the ignition switch.

I have a degree in electrical engineering, so I 'm qualified to do any level of electrical troubleshooting that may be required. I'm just hoping for some advice that can point me toward the right areas.