Check the wiring diagrams in the shop manual if you have one. See what the instrument cluster and ABS is run off of. If they both share a same system, it could be the problem.

There's relays and such near the ABS on the passenger side of the engine compartment. Start up the car and listen to see if its coming from that area. I believe the ECU for your car is under the flooring of the passenger front seat where it meets the firewall (at least it is on my 93, and they're very similar even if the body's different). You should be able to peel back the carpeting where it terminates under the dash to reveal a metal kick panel behind which resides the ECU. You may have to remove some plastic paneling in the footwell to get the carpet to peel back well.

Keep in mind I'm basing this off the 4th gen, and not the 5th gen Accord, and some of the info may be inaccurate. Both generations share many parts. Good luck.