A DISTRACTED CL65 PIC TURNS THE WRONG WAY DURING TAXI IN; A TXWY INCURSION; AT DTW; MI.

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WE HAD JUST LANDED AT DTW ON RWY 22R AND CLRED AT TXWY A4. WE WERE GIVEN A TAXI CLRNC OF TXWYS Q; T; Y V. DURING THE TAXI; WE HAD A JUMP SEATER WHO BEGAN TALKING AND I DIDN'T CORRECTLY ASK HIM TO STOP. I GLANCED AT THE TXWY DIAGRAM AND THOUGHT THAT I SAW THE PROPER TAXI RTE. MY FO BECAME DISTRACTED WHEN A SWITCH COVER FELL OFF THE COCKPIT OVERHEAD PANEL JUST AS WE REACHED INTXN T. I TURNED R INSTEAD OF L AND IT WAS THE JUMP SEATER THAT POINTED OUT THE MISTAKE. GND CTL THEN TOLD US TO JUST MAKE A 180 DEG TURN AND GET BACK ON COURSE. THERE WERE NO CONFLICTS; FORTUNATELY. SUPPLEMENTAL INFO FROM ACN 536261: THE TURN OFF OF TXWY Q TO TXWY T IS A L TURN TO JOIN TXWY Y; BUT WE INADVERTENTLY TURNED R BECAUSE THE CAPT WAS CONFUSED. I WAS TRYING TO FIX A GUARDED SWITCH THAT HAD COME LOOSE WHILE ENRTE AND CONSEQUENTLY I WAS NOT PAYING ATTN TO THE TURN OFF OF TXWY Q. WE ALSO HAD A JUMP SEAT THAT WAS CONVERSING WITH ME AS TO HOW TO FIX THE PROB. THE COMBINATION OF A CONFUSED CAPT AND AN FO DEALING WITH A PROB AT THE WRONG TIME WITH A LACK OF STERILE COCKPIT CONTRIBUTED TO THE WRONG TURN.