C560XL CREW HAD A TRACK DEV AFTER THE ACFT RAN OUT OF NOSE DOWN TRIM CAUSING AN APCH OVERSHOOT AT CLT.

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THIS FLT HAD DEPARTED AGS FOR CLT. ALTHOUGH THE TRIM INDICATOR WAS PROPERLY SET FOR TKOF; AN EXTREME NOSE UP TRIM CONDITION EXISTED AFTER LIFTOFF. WE MANUALLY TRIMMED THE ACFT AND CONTINUED TO CLB. WHEN FLAPS WERE SELECTED TO 7 DEGS; THE ELECTRIC ELEVATOR TRIM WAS RUN FULL NOSE DOWN IN AN ATTEMPT TO TRIM THE ACFT. HOWEVER; IT STILL EXHIBITED TENDENCY TO CLB. I WAS CLRED TO INTERCEPT THE LOC FOR RWY 36R; BUT WAS PREOCCUPIED WITH MY TRIM PROB AND FLEW THROUGH IT. APCH TURNED ME BACK TO THE NW TO REINTERCEPT. I ONCE AGAIN FLEW THROUGH THE LOC INTO AIRSPACE USED FOR RWY 36L. BECAUSE OF MY FIXATION WITH THE TRIM PROB; I HAD FAILED TO ARM THE LOC ON THE CAPT'S SIDE AND WAS NAVING ON THE FMS. I SIMPLY MUST REMEMBER TO FLY THE BASICS WHEN SYS ARE ABNORMAL WITH THE ACFT. I SHOULD HAVE RPTED TO ATC THAT I HAD A PROB WITH THE ACFT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE CAPT RPTED THAT THE TRIM INDICATOR WAS OUT OF THE PROPER TRACK IN THE TRIM WHEEL. IT INDICATED FALSE TRIM SETTINGS. MAINT GOT THE TRIM INDICATOR BACK IN THE PROPER TRACK; AND TIGHTENED IT SO THAT IT WOULD NOT JUMP THE TRACK AGAIN.