Tail light mounted of '89 Accord fails to work

First thing I would check is all frame grounds... like the negative battery cable and the grounding strap on the passenger side motor Mount to the wheel hub. In any electrical system, lights draw more current than anything (except the battery) when you turn them on... Check the grounds!

Leaking trunk seal or rear window sealer also check the tail lights are mounted properly and that the trunk is closed all the way

You will need to check wiring at the sockets, turn lights on and remove the tail lights from tail lens and wiggle bulb to see if they will light up . this is to see if its a connection in the socket.

Another area to check is to open the hood and check the wiring going to rear lights, look toward the driver side trunk hinge and check for broken wire or wires. this is a common area for wire damage. look closely.

The bulb check unit, which detects when the rear lights are blown, is malfunctioning or has gone totally bad. It's located inside the trunk mounted, drivers side tail light assembly. Have it checked out and repaired if necessary.

It's located inside the piece of taillight that's mounted on the drivers side trunk lid.

There is a bulb check module mounted, I believe, on the inside of the drivers side trunk mounted tail light. Power first has to go through this module before going to the various different tail and brake lights. Check the circuit board inside that module for shorted circuit lines, as it seems to be a common problem with those years Accords.

If water is in the trunk, then it is probably getting in through the rear tail lights. Common problem with early 90's Honda cars. To check, hose down the trunk area and tail lights, then look at the gaskets from inside the trunk. You'll probably will see some water. To fix, you need to take each tail light out and place a seal of silicon caulk between the body of the car and the tail light gasket and replace the tail lights. This should solve your water in the trunk problem.

The brake light on the trunk is call a Back Up lamp Applique,
Hope this was very helpful.

Alot of these cars you need to remove the panal inside the trunk to access the nuts that hold the assembly on. Also you usually do not need to remove the assembly to change a lightbulb. .

Hope this was your question because you really didn't ask a question, You made a statement.

You remove the tail light by removing the nuts or bolts from inside the trunk area. This is what holds the tail light in place.