There are a couple of possibilities. One is lack of lubrication of brake system moving and/or contact points such as between back of pads and caliper housing and/or piston. Another could be that, the rotors/discs are warped/distorted and need to be machined or more preferably, replaced.
If you replaced the front brakes (example) and you still have a squeal, it's possible it may be coming from the rear brakes.
Automatic transmission fluid does not squeal. You have a different problem. Brakes squeal, bearings squeal, and belts squeal. Fluids do not squeal. You had better take your vehicle to a mechanic.
hypothisies
hypothisies
Bad logic
theory
Sounds like low pads. many have built in wear indicators that squeal to warn you.
This can be a normal situation or mechanical problem. Some brakes had natural squeal regardless of pad life or lubricant used. However many brake systems have squealers which make a sound alerting the pad life is at replacement stage.
A slipping belt or some kind of air flow problem..
At least inspect when you hear squeal. Base further work on what you see.
Then you should get a cat. The problem is not a mouse- the problem is that your brakes are wearing out. They are designed to make a noise to tell you that. Skip the cat, take your car to a shop where a mechanic can replace the worn parts. They can check for mice at the same time.
Wishful thinking, as a trapped mouse is cheaper than getting a garage to sort your brakes out - probably the pads need replacing.
Due to dust getting in between pads and rotor