That clicking sound behind the glove compartment could be the factory security system engaging the kill-starter feature, according to a forum thread I read elsewhere, too. That happens sometimes including when you change or disconnect the car's battery or otherwise trigger a sensor (there are many).
You may be able to reset it with the reset button by the drivers side fuse box, or the factory radio or driver door lock with a key fob, sometimes in combination with the driver's power (un)lock button. If you have the factory security system you'll need the factory radio and/or the factory fob (discontinued and hard to find) not an after-factory replacement, and the original security code. I have heard of other tricks too like removing then replacing the radio fuse, disconnecting the battery, touching the disconnected battery cables together and such but that didn't help me. because my radio appears to be dead.
Do internet searches using terms like: factory accessories, security, alarm, reset, deactivate, reprogram, stereo, radio, computer, fob, remote, transponder, transmitter, valet button, reset button, panic button, programming, immobilizer, kill-starter, VIN, brake code, security code, serial number, anti-theft code, radio identification card
NOTE: many of these terms are interchangeable and I can't imagine why there aren't standard terms used at least by Honda staff (unless there are in the manuals, idk),
I found it helpful to talk to a Honda dealership parts and service staff, a stereo store installer, a locksmith, and a tower at a junkyard to learn about this initially. Most recommended towing to an electrical diagnostic shop, which I am trying to avoid paying for, but maybe you can manage this in your case.
Here are just some of the links I found in many hours of searching, reading, and viewing youtube. I cannot vouch for the info I repeated above or found in these threads or sites. I am just trying to consolidate some info so other owners and service personnel can find it when troubleshooting. Honda has pages too (but I'd need to go back in my history to find more). No I don't work for any of these fyi
http://www.fixya.com/cars/t3158204-need_unlock_honda_accord_1995_radio
http://www.bcae1.com/
http://locksmithcharley.com/transponder/acura-honda.shtml#Start
https://www.youtube.com/watch?v=bwTfV3sJ8os
https://www.2carpros.com/questions/honda-accord-1995-honda-accord-security-system