Having the vehicle checked for DTC'S -diagnostic trouble code's , In all the module's on the vehicle ! Not just OBD2 engine code's . BCM - body control module ,radio , HVAC - heating an A/C control panel . All these thing's can have DTC'S . If no DTC are found the next step ,viewing wiring diagrams to see if these share a gound or B+ voltage supply ! Do you know what a body or chassis ground point is ? The brake pedal position sensor is an input to the BCM . The brake light's are turned on by a high side driver ( transistor ) inside the BCM . As are the turn signal's . The radio an the HVAC controls - heating an A/C are tied together . But do not share any circuit's with the BCM or the turn signals or the brake light's . The turn signals , brake light's an the BCM share a common grounding point G403 . Can't really see why using the brakes an turn signal's would cause the radio an A/C to turn off . Wouldn't be fuse's , nor the battery , more thing's wouldn't be working . Your best bet mite be to take it to a qualified repair shop an pay an hour dignostic time . Or bring it to me . If i can't find the problem in an hour i won't charge you . Do you know anything about automotive electrical systems ? Looking at wiring diagrams , using a DVOM - digital volt ohm meter to test the electrical circuit's . Free wiring diagrams here
http://www.bbbind.com/free_tsb.html Enter vehicle info. year make , model an engine size . Under system click on lighting ,then under subsystem click on stop lamps . Click the search button ,then the blue link's one at a time .
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Testing an not guessing is how to find electrical problems .