Blown fuse

Which is it, a 1961 Chevrolet Biscayne or a 1938 Studebaker?

The first thing to do would be to find a wiring diagram and none of the online access repair manuals that I use have something that old.
Would you happen to have one?
Also, you never mentioned which model Studebaker this was.
I was not aware that a brake light switch was on the master cylinder.
There is only one website that I know might have it, so let me check there. http://www.oldcarmanualproject.com/

No luck.
If you updated the wiring anyhow, I doubt then if the original wiring would be accurate now anyhow.
Remove the fuse, remove all the bulbs, then check again for a short to ground on the backend of that fuse socket. If the light switch is down line from the fuse disconnect it and test again. Make sure you remove all the bulbs, too, the brake, tail, license, backup as well as any interior lights.

You may be able to insert an automatic resetting circuit breaker into that fuse socket then with all the bulbs in check to see if one or more do not work, then it may help you narrow down the circuit that is shorted.

Hi guys. Please allow me to add a couple of comments of value that might make this easier. The brighter filament in an 1157 bulb draws very close to one amp, so three would draw three amps. A ten-amp fuse would be fine as it has more than a twenty percent safety margin. A 15-amp fuse will not cause a problem here because you most likely have 14 gauge wires, and they can handle 15 amps continuously. Brake lights are only used intermittently.

Even better than an auto-resetting circuit breaker, take one of the blown fuses, solder about a three-foot piece of wire to each end, then solder the other ends to the two terminals of another 1157 or 3157 bulb so you're using the brighter filament. Be quick when soldering to the fuse. Too much heat for too long will melt the glue, then the metal caps will slide off. If your rewire job uses the newer spade-type fuses, grind off enough of the plastic so you can solder to the tops of the two terminals. You can also just use a pair of universal crimp-type terminals, and plug them in individually in place of the blown fuse.

When the circuit is turned on and the short is present, the test bulb will simply be full brightness. It will naturally get hot too, so do not let it lay against door panels and carpet. Now you can take your time and unplug stuff and move wires around to see what makes the short go away. When it does, the 12 volts will divide up between the test bulb and those in the circuit, so the test bulb will become dimmer or go out.

As a thought of places to look, we used to see a lot of chewed-up trailer wiring harnesses. If you have that on the car, check for frayed brake, tail light, and ground wires shorted together. If you have an older U-Haul harness with three red leds in the connector to show at a glance which circuit is for which wire, it was real common for those plugs to become shorted internally.

Also, look closely at an aftermarket third brake light assembly. Some of them have one terminal connected to a mounting screw hole to provide the ground, but it is possible to connect your 12 volt feed wire to that, then run a ground wire from the other terminal. That will put a dead short on the brake light circuit until that housing is unbolted from any sheet metal. Part of the body.

I have not thought this through yet, but do not overlook a shorted or incorrect turn signal switch if the same rear bulb is used for the brake light and the turn signal function.

First remove all three of the brake light bulbs, then see if the fuse blows as soon as you press on the brake pedal. If so and you had no continuity to ground on that circuit then perhaps it is a shorted brake light switch.
If the fuse does not blow, put the bulbs back in one at a time to at least narrow it down to which bulb circuit it is. Then inspect that circuit for a shorted wire.

Question, is the turn signals on this oldie but goodie work on the same filament as the brake lights? If it does, do the turn signals work?

Roy