2006 Honda civic coupe does not have an external trunk lock & inside lever does not open either. I can hear trunk try to open when I use the remote.
2006 Honda Civic Coupe EX, Trunk will not open. on 2006 Honda Civic
Not sure if that car may have a valet switch in the glove box check your owner's manual. It may be necessary to remove the interior trim panel from the hatch to inspect the locking mechanism.
There is a dual purpose lever by the drivers door that both opens the trunk and is for the gas fill. It opens the door to fuel, but not the trunk.