I'll try to explain this as best as I can since I am no electrical expert.

My brake/tail lamps contain 2 1157 bulbs each. When I turn on the lights, one is brighter than the other. But when I step on the brake, it is vice versa.

I replaced the original bulbs with new 1157 LLs because they were corroded, but this didn't fix the problem.

I also checked the fuse for the brake lamp. It's fine.

What could be the problem?

. Disconnect the negative. Battery cable.
. Thoroughly clean all corossion from each socket and spray with WD-40.
. Clean brake light switch and spray with WD-40.

You have one circuit for the parking lights and another for the brake lights. The difference in brightness is a function of resistance in each circuit. A test light or multimeter should help you locate the problem.

Start by replacing sockets. You need clean bulbs and clean sockets. Or clean effectively.
Try putting on 4 way flashers and walk around, noting front and back brightness.
Your brake switch sounds OK.
From the brake switch, it goes through the Signal Head(Turn signal switch) then to
Tail/Brake lights.
Check bulb socket and make sure bulb oriented correctly(Not 180 degrees out)
Corroded socket may allow bulb to be inserted incorrectly.
And verify your socket has good continuity with ground. Good Luck