I have a 2006 XC70 that has all brake lights out but I have replaced bulbs, fuses, a new REM, a new tailgate wiring harness, new brake pad sensor, new brake light switch, and the vacuum brake pump.

I’m at a total loss of ideas at this point as to what could possibly be causing them to not light up so hoping for some ideas here!

 

Do you have 12v at the brake light sw? (with your $5 test light) Does the 3rd brake light work? The CEM might send the "turn on the brake lights" signal on the canbus to the REM - Water intrusion is ~common with the CEM - have you checked the CEM for water intrusion/damage?
Or does the brake light signal go on a physical green/yellow wire from terminal a:15 on the CEM to terminal a:18 on the REM - then exits to the left and right bulbs at terminal b:3 on the REM?