Just for grins, switch the left and right Tail Light Bulbs. If there's no change, then at least you know that the Bulb is OK, but if the problem moves to the right, then check to be sure you have the correct Double Filament, (1157), Bulb and/or try a new Bulb.
Other than that, there are any number of areas that could be the cause as already mentioned by previous responses; a good digital volt meter may become your best friend to help with this issue.
All the best.
Ray