PA31 PLT EXPERIENCES AN ENGINE FAILURE ON APCH DUE TO FUEL STARVATION AFTER A WX RELATED DIVERSION.

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I WAS FLYING A PART 135 CHARTER FLT TO ZZZ CARRYING CARGO AND 1 PAX. THE PLAN AFTER THAT WAS TO FLY TO ZZZ1 FOR FUEL AND THEN RETURN TO BASE. THE FLTS AFTER ZZZ WERE CONDUCTED EMPTY UNDER PART 91 OPS. THE WX ENRTE WAS VFR EXCEPT FOR THE APCH INTO THE ARPTS. THE FLT INTO ZZZ WAS UNEVENTFUL. PRIOR TO DEP TO ZZZ1; THE WX AT THAT DEST WAS 500 FT AND 10 NM. AFTER CHKING ATIS; THE WX HAD DROPPED TO 400 FT 10 NM. I ELECTED TO FLY THE ILS APCH TO RWY 9. WX REQUIREMENTS FOR THE APCH WERE 300/3/4 NM. WHILE ON FINAL TO THE RWY THE WX CONTINUED TO DROP 300/5 THEN TO 200/5. I DID NOT BREAK OUT AND INITIATED A MISSED APCH. I REMAINED VFR AND REQUESTED A SPECIAL INTO THE FIELD FROM THE OTHER SIDE OF THE ARPT. ANOTHER ACFT WAS IN FRONT AND HAD RPTED GOOD VISIBILITY FROM THAT DIRECTION. AS I BEGAN TO INITIATE THE SVFR; THE WX DROPPED FURTHER TO 1 NM VISIBILITY. I ELECTED TO DISCONTINUE THE SVFR AS I WAS NOT FAMILIAR ENOUGH WITH THE FIELD TO SAFELY CONTINUE. I CLBED BACK INTO VFR CONDITIONS AND REQUEST WX FOR ZZZ2. THE WX FOR ZZZ2 WAS VFR AND THE ENRTE WX WAS VFR AS WELL. I ELECTED TO PROCEED TO ZZZ2 AS THE PLANNED ALTERNATE HAD NO SVCS AVAILABLE AND I KNEW I WOULD NEED FUEL. ZZZ2 WAS 155 MI FROM MY PRESENT POS AND 54 MINS ACCORDING TO THE GPS. BASED ON THE FUEL QUANTITY INDICATION AT THE TIME; I CALCULATED I HAD 250 LBS OF FUEL. MY BURN RATE WAS 3 LBS PER MIN WHICH WOULD GIVE ME 92 LBS REMAINING UPON ARR AT ZZZ2. WHILE ENRTE TO ZZZ2; THE GND SPD DECREASED AND THE RATE OF FUEL DROP IN THE R FUEL GAUGE ACCELERATED PAST THE FUEL IN THE L FUEL GAUGE. AS I BEGAN THE VISUAL APCH INTO ZZZ; MY R ENG FAILED DUE TO FUEL STARVATION. I DECLARED THE EMER AND CONTINUED THE APCH AND LNDG UNEVENTFULLY. I ALLOWED MYSELF TO MISJUDGE THE FUEL BURN ON THE WAY TO ZZZ AS I WAS ABLE TO MAKE IT ON MY OUTBOARD FUEL TANKS UNTIL FINAL APCH. THIS LEFT ME APPROX 2 HRS 30 MINS REMAINING ON NORMAL FUEL BURN RATES. HOWEVER; NEW COMPANY POLICY HAD US FLYING REDUCED PWR SETTINGS. I ALLOWED THIS AND THE CONCERN ABOUT FUEL SVCS AVAILABLE TO CLOUD MY JUDGEMENT. I ALSO ALLOWED MYSELF TO BE DEPENDENT ON THE FUEL QUANTITY GAUGES. THIS; ALONG WITH ALL OF THE OTHER FACTORS; LED ME TO MAKING A POOR DECISION TO PRESS TO ZZZ2 VERSUS GOING TO MY PLANNED ALTERNATE. THE RESULTS OF THE INCIDENT HAS INITIATED A NEW COMPANY POLICY FOR THE ROUTING TO SUCH REMOTE LOCATIONS. WE ARE NOW REQUIRED TO PROCEED TO ANOTHER FIELD FOR FUEL BEFORE DEPARTING TO ZZZ. THIS ALLOWS FOR 1 HR MORE OF FUEL AND BETTER PLANNED ALTERNATES.