They are in parallel so no. Does your front park lights turn on? If they don't check fuse 10 (15 Amp).
Since your brake lights and backup work this eliminates a ground problem.
Take a look at this:
If your front lights are working I think it would be safe to assume that the problem is around connector C118 (circled in red, located at the drivers side rear of engine compartment). But this same connector feeds your brake lights etc too.
What you need to do is find this brown wire and follow it with a test light to see where its getting power and when it stops.