RWY CHANGE. FMC NOT PROGRAMMED; GAR.

Narrative

I WAS THE CAPT AND FLYING THE ACFT INTO BRU-EBBR. ATIS RPTED LNDG ON RWY 25L. DUE TO A BUILDUP; WE WERE SENT N OF THE PUBLISHED ARR. HEADING E; WE WERE DOWNWIND AND N OF THE ARPT FOR A R BASE TO RWY 25L. APCH THEN CHANGED OUR LNDG RWY TO RWY 25R. WE RE-SELECTED THE ILS TO RWY 25R AND IDENTED IT. WE WERE THEN GIVEN A HDG TO INTERCEPT THE LOC; AND CLRED FOR THE APCH TO RWY 25R. WHAT WE HAD NOT DONE IN OUR HASTE WAS TO CHANGE THE RWY/ILS SELECTED IN THE FMC; SO THE MAP DISPLAY SHOWED THE EXTENDED CTRLINE OF RWY 25L. FALSE LOC CAPTURES ARE A KNOWN PROB AT BRU AND I HAD SEEN THAT A FEW TIMES; ONCE EARLIER IN THE MONTH FOR RWY 25L. THE AUTOPLT WAS IN USE AND THE LOC WAS CAPTURED. I LOOKED AT THE MAP DISPLAY AND SAW WE WERE STILL WELL R OF THE CTRLINE. SO I STATED OUT LOUD THAT I THOUGHT WE HAD A FALSE LOC CAPTURE AND RETURNED TO THE INTERCEPT HDG. WE WERE IMC IFR IN THE CLOUDS OF A PASSING SHOWER WITHOUT VISUAL CONTACT WITH THE ARPT. AT SOME POINT; APCH ASKED IF WE KNEW THAT WE WERE CLRED TO RWY 25R; THEN TURNED US TO THE R TO HDG 280 DEGS TO INTERCEPT THE LOC. ABOUT THIS TIME; THE SECOND COPLT SAW RWY 25L WAS ON THE MAP. AT THAT POINT; THE CLOUDS BROKE SOME AND I COULD SEE RWY 25L. AFTER REACHING THE RWY 25R LOC I COULD SEE THE RWY CLRLY. I FELT THE WORKLOAD INCREASING AND THOUGHT IT WOULD ADD TO THE CONFUSION. I ELECTED TO MAKE A MISSED APCH. I BELIEVED WE WERE TOO FAST AND A LITTLE HIGH. THIS CAUGHT APCH CTL BY SURPRISE; BUT WE WERE THEN ISSUED VECTORS FOR ANOTHER APCH TO RWY 25R.