iam not sure on 88's! but i know like around 90ish accords they have left and right brake light sensors. Does the high mount or third brake light come on also? Continously? And you said that the right side stays on all the time? Blinkers don't work etc.. But the brake lights stay on. I would do a continuity check between the brake sensor and high mount brake light, and both inner and outher brake light on the right side. I would say that if you don't get a complete circut you probably have a short in the brake light sensor. Unless you think you have a break in wires like accessories etc.. that you might have or seen installed? Or you could maybe just swap left to right brake sensors and see if the left side does what the right side did? The brake sensor is located on the body panel were the tail lenses go.

It would be best for you to get a etm so you can see where iam talking about. Because there are several connectors for you to check. Someone else might have a better way though for check this.

I couldn't imagine this being a brake switch because only your right side brake lights stay on.