B727 WITH FLT INST PROBS RESULTS IN CREW FLYING THROUGH LOC ON ILS APCH.

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ON R DOWNWIND TO RWY 26 BOTH CAPT AND I SWITCHED FROM GPS MODE TO VOR/LOC ON NAV SELECTOR. APCH CHK WAS RUN AND RADIOS TUNED AND IDENTED. APCH GAVE ME A 230 DEG HDG TO INTERCEPT THE RWY 26 LOC. THE LOC ON THE R SIDE NEVER HAD CASE BREAK BUT THE CAPT'S LOC DID. NEITHER OF US CAUGHT IT. BECAUSE WE WERE IN A BROKEN LAYER THE CAPT WAS LOOKING OUT THE WINDOW AND DID NOT NOTICE CASE BREAK ON HIS LOC NEEDLE. I WAS INSIDE ON MY INSTS AND MY LOC NEEDLE DID NOT MOVE. APCH CALLED AND TOLD US WE HAD FLOWN THROUGH THE LOC. AT ABOUT THE SAME TIME WE BROKE OUT OF CLOUDS AND SAW THAT WE WERE ALMOST LINED UP ON RWY 27. I BEGAN THE R TURN BACK TO RWY 26 AND RECYCLED VOR/LOC/GPS SWITCH. WHEN I DID THAT THE LOC NEEDLE SHOWED FULL SCALE DEFLECTION TO R. THE CAPT STATED THAT THAT HAD HAPPENED TO HIM BEFORE. WHEN GPS/VOR BUTTON IS PUSHED THE INDICATION IS THAT NAV MODE HAS CHANGED WHEN IN FACT THE MODE HAS NOT SWITCHED AND THEREFORE THE OBS NEEDLE READS THE WRONG INFO. ON MY PART; I SHOULD HAVE XREFED THE CAPT'S INSTS AND HE ALSO SHOULD HAVE MONITORED HIS MORE CLOSELY.