The real problem with the Subaru Outback's burning smell

in case it might help (although you think your problem is differential fluid, not brake fluid):
My 96 subaru had a very small leak of brake fluid. Location was at a connector that joined two pre-formed brake lines. The connectors were located in the engine compartment, I think somewhere near the engine wall over the right front tire area. When it dripped, drips landed on part of the exhaust system below.

Note that a minor brake leak might only occur when you press on the brakes hard enough to raise brake line pressure – say when you slow down rapidly on a highway off ramp. So a leak might be intermittent, depending on your use of the brakes.