MALFUNCTIONING STABILIZER TRIM ON C340 DISRUPTS PLT'S CONCENTRATION ON VISUAL APCH TO RWY 19 AT TEB. ALTDEV AND 360 DEG TURNS IN WRONG DIRECTION RESULT. SUBSEQUENT APCH IS UNSTABLE AND RESULTS IN LONG BUT SAFE LNDG.

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UPON ARR AT TEB THE APCH CTLR WAS USING THE VOR-DME A APCH AND WE WERE ASKED TO KEEP SPD UP UNTIL XING OVER THE TOP OF RWY 19 TO MAKE A L DOWNWIND FOR RWY 19. AS I CROSSED OVER THE TOP; I WAS DSNDING TO 1000 FT FOR THE DOWNWIND LEG. AFTER THE PRE-LNDG CHKLIST ABEAM FROM THE RWY NUMBERS; I TOOK THE AUTOPLT OFF; BUT SLOWLY WE CLBED BACK TO 1500 FT. TURNING BASE; THE CTLR TOLD ME TO DSND BACK TO 1000 FT. I NOTICED THE ELECTRIC TRIM WAS SLOWLY RUNNING IN THE 'UP' POS. AS I TURNED TO FINAL APCH; I PULLED THE TRIM BREAKER AND ASKED TO GO AROUND OR MAKE A 360 DEG TURN TO LOSE MORE ALT. THE CTLR SAID TO MAKE A 360 DEG TURN. I BELIEVED HE SAID 'R' BUT WAS TOLD LATER HE SAID 'L.' JUST BEFORE THE TURN; HE SAID THAT THERE WAS A TV TWR AT 1200 FT TO MY R; SO I THOUGHT I WAS GOING TO THE CORRECT DIRECTION AND MAKE SURE I HAD IT (TWR) IN SIGHT; WHICH I SAID I DID. DURING THE GAR; I CLEANED UP THE ACFT; FLAPS AND LNDG GEAR. AT THIS POINT HE REPEATED THAT I COULD LAND ON ANY RWY. I WAS GETTING ALIGNED UP AGAIN FOR RWY 19; COMING AROUND FROM THE E 360 DEG TURN. THE MANUAL TRIM WORKED FINE BUT THE LNDG WAS A VERY SHORT FINAL; 1/2 MI. AS I DSNDED THROUGH 575 FT; I AGAIN LOWERED THE LNDG GEAR AND SECONDS LATER THE TWR ASKED IF I HAD MY LNDG GEAR DOWN AND I TOLD THEM IT WAS IN TRANSIT. LANDED AND ROLLED OFF TO THE FBO. WITH THE EXCESSIVE SPD ON THE APCH WHEN I WAS ON DOWNWIND; I SHOULD HAVE ASKED TO EXTEND MY DOWNWIND. THAT WOULD HAVE HELPED ME BLEED OFF SPD AND THEN GIVE ME ADDITIONAL TIME TO TROUBLESHOOT THE TRIM. ONCE ON THE GND; I PUT THE BREAKER BACK IN AND TRIED IT AND NOTICED THAT THE SWITCH ON THE YOKE CTRED ITSELF. I DON'T THINK IT HAD CTRED BACK TO NEUTRAL POS. I PLAYED WITH IT FOR 5 MINS OR SO AND COULD NOT GET IT TO REPEAT THAT BEHAVIOR AGAIN. ADDITIONALLY; FOR THE PAST 8 MONTHS OF FLYING THIS ACFT; THIS NEVER HAPPENED BEFORE EITHER. SINCE I DEVIATED FROM NORMAL OPS; I HAD TO WORK HARDER TO GET BACK INTO FINAL AND LAND NOT GIVING MUCH ROOM FOR ERROR. ALSO; THIS WAS MY FIRST TIME AT TEB ARPT.