Definitely the switch in the shifter position...

There is a momentary switch to turn on the reverse / backup lights.  The switch as mentioned in the previous post, stuck in "on" position.  If the wiring around the bulbs is shorted, it would blow the fuse and not leave the lights on. 

Check into the switch... if you do it yourself, it's a matter of few bucks.. switch might cost around ~20 or $30 max... I can't imagine it being more than that... I really do not know the price.