Back lights and dashboard lights don't work; brake lights and headlights okay. Bulbs are okay. Does it have anything to do with the dimmer relay and what does the dimmer relay do?

First, test all under-dash and under-hood fuses with a test light or multimeter. Here's how:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-46563-3.html#post252145

Second, the Dash Lights Brightness Controller controls gauge lights, A/T Gear Position Indicator Dimming Circuit, Hazard Warning Switch Light, Rear Window Defogger Switch Light, A/T Gear Position Console Light, and Heater Control Panel Lights. It's normally located on the dash, just to the left of the steering wheel.

Third, the A/T Gear Position Switch (back-up light switch) controls back-up lights.