if the brake light not working the Part # 912 ( Bulb needed) at advance auto parts $4 for the bulb, replace the bad bulbs there will be 3 of them in there .
1- if that don't work , then go to the BCM , internal relay be bad, but not serviceable, so module replacement will be needed if that is the case .
I sent you location picture of the BCM , press on the blue link to view pictures ,there is 2 diagrams , # 7 is the BCM in one & # 8 in the othere diagram , same part just different view of the location of it
2- switches is problem but yours seems to work when press them ,so these should be good .
3- Do an ECM reset , by disconnecting the battery for 15 minutes and see if it a matter of resetting the module ,if none the above worked .
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