Increase ur fuse rating to 15A.
Don't worry too much wire burnt.
Even 25A fuse will burnt easily if short circuit.

Increase ur fuse rating just to check wether ur extra brake light consume enough current or not.

FYI..i changed to air horn, and after few horn, the fuse burnt.
Change to higher rating fuse solved this problem.

Last but not least, wire can hold up to 100A, not a problem, fuse is for safely.

Update us what's ur solution~