Since I am short of ideas on connection between brake light and fuel gauge not functioning (other than fuse problem), i would investigate the brakes lights first.
Start with replacing one of the bulbs in the lamp. Chances are one was blown some time ago, one has been blown recently. If that does not help:
check other fuse 5 devices (ignition on):
- do the turn signal indicators work?
- does the reverse light work?
If not - something is wrong with fuse 5.
If yes, then:
If you have a multimeter - use it now, if not, just get a 12V bulb with holder and two wires, hook one wire to ground and check with the other wire, having switched on the ignition:
- do you have power on fuse no. 5? probably yes
- do you have power on one of the connectors at the stop lights switch? if yes
connect the connectors together and check
- do you have power on the bulb holder in the lamp? check this carefully - some lamps have the bulb base made of two layers of metal, you may have power on the bottom metal layer, but not on the top one, on which bulb rests
if no - something happens on the way of the wire, I guess.