So the challenge has been issued!
The brake light switch you replaced should have 4 wires connected to it.
Pin #1 Green/White
Pin #2 Red/White
Pin #3 Green/Black
Pin #4 Either Red/Yellow or possibly White
1) Use a voltmeter and measure the voltage on the Red/White wire. It should measure 12volts whether the ignition is on or off.
2) If you don't read 12v then check the fuse again. Sometimes the labels in the fuse panel make it confusing as to which fuse is which. You are looking for a 10A fuse labelled "STOP". It should be red in color.
3) If you do read 12volts, then connect this red/white wire to the green/white wire ( use a short wire or paper clip to do this). Your brake lights should come on.
If the lights come on in step #3, your new switch is still defective, or it is not mounted correctly, and as a result it is not operating when you step on the pedal. Try operating the switch with your finger to test that possibility. You could also remove the wiring harness from the switch, and place your ohmmeter probes into the switches connector on pins #1 and #2. The resistance should read 0 ohms when you step on the pedal.
Let us know the results.