The 15 amp fuse that controls the stop lamps and high mounted stop lamp blows out at least once a month...before and after I switched over to leds, so leds are irrelevant.

It always seems to happen when I have the lights on, rear fog lights and am reversing. Should I put a higher amp fuse?

 

I dont believe a higher fuse would be wise. If you are using LEDs then current draw would low and blowing fuse shows other issue. If you increase fuse size you could melt wiring and/ or start fire.
I would dismantle and clean lamp sockets, any wire connections and grounds. Check out condition of brake switch also.

 

Are they are correct size? You pretty much need to look through the whole circuit and find out what the extra resistance is from. Just make your way around checking resistance until you find the bad spot

 

I'm thinking you've overloaded a circuit. Which of these is non-stock?

Are the rear fog lights an add-on? Are they wired into the tail light circuit? Does this fuse also operate the back-up lights?

Look at the fog lights. You have a predictable overload in that circuit as it happens when all 3 are in operation; maybe even a dead short in one of the wires.
(';')

 

No don't put a higher amp fuse in, use the correct rating.

You most likely have an intermittent short.

If you have a 100w incandescent light globe wire it in parallel with the fuse, (this will prevent the fuse from blowing). Then go around a wiggle all of the brake light wiring including the switch on the pedal.

If the globe lights when you wiggle a wire you have probably found you problem.