Your rear lights function ONLY as blinkers and not running lights like the front ones. Completely normal. As for the tail light, if everything is in order with the socket and the proper bulb being used and it is inserted properly, I would look under the fender at the tail light harness. They frequently come loose and rub through the insulation or the rear wheel will rub through it. Start under the seat where it goes through the hole in the rear fender and follow the harness to check it out. If you unplug the plug under the seat where it goes through the fender and test ride it being careful you don't get rear ended with no brake light, you will probably not blow any fuses then.