FLT CREW OF BE40 DIVERT TO ANOTHER ARPT WHEN LNDG GEAR SAFE LIGHT FAILS TO ILLUMINATE AT ASE.

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ON OUR WAY TO ASE; WE HAD 2 SETS OF DELAYING VECTORS. AFTER FINALLY BEING CLRED FOR THE ROARING FORK VISUAL (APCH TO ASE) I CALLED 'FLAPS 20 DEGS' AND A MOMENT LATER; 'GEAR DOWN.' THE L-HAND GREEN GEAR LIGHT DID NOT ILLUMINATE AFTER THE GEAR LEVER WAS MOVED DOWNWARD. I RECYCLED THE GEAR AND AGAIN NOTICED NO CONFIRMING LIGHT ON THE L-HAND GEAR. I WAS DSNDING THROUGH 11000 FT HAVING JUST PASSED DBL VOR. EVEN WITH ASE IN SIGHT; I ELECTED TO DISCONTINUE THE APCH INTO THE ASE VALLEY; CLB AND RESOLVE THE MATTER. EVEN THOUGH WE WERE NOT ON THE VOR OR LOC APCH; I CLBED TO THE R TO INTERCEPT THE PKN LOC. MY FO INFORMED ASE TWR OF OUR DECISION. BACK WITH ZDV; WE CLBED TO 16000 FT AND INFORMED THEM THAT WE WANTED TO DIVERT TO EGE AND THAT MOMENTARILY; FUEL WAS GOING TO BECOME AN ISSUE. ALTHOUGH I NEVER DECLARED AN EMER; ATC REPEATEDLY TOLD OTHER TFC THAT WE WERE IN AN EMER CONDITION. I EXCHANGED THE R-HAND GEAR BULB FOR THE L-HAND GEAR BULB AND TOOK ONE ADDITIONAL STEP OF LOWERING THE GEAR TO CONFIRM THAT NOW THE L-HAND BULB ILLUMINATED; BUT NOT THE R-HAND. I INFORMED ATC AND OUR PAX OF THE SITUATION; TELLING THEM I WAS MERELY 'PLAYING IT SAFE' ON ALL ACCOUNTS. ATC PUT US ON A VECTOR AWAY FROM EGE AND JUST A MOMENT LATER I DECLARED 'MINIMUM FUEL.' I WAS AT 1100 LBS OF FUEL; BUT FELT THAT ANY ADDITIONAL DELAYS WOULD NOT LEAVE MY ANY OTHER OPTIONS. A MOMENT LATER; ZDV GAVE US A CLRNC HEADING TOWARDS THE LOC APCH TO EGE. ON SHORT FINAL; MY FO QUESTIONED THE TWR WHO CONFIRMED THAT ALL 3 OF OUR GEAR 'APPEARED DOWN.' LNDG AND TAXI WERE UNEVENTFUL. ON TAXI IN; I OVERHEARD EGE GND CTL TALKING WITH A FIRE TRUCK AND I DID SEE ONE CROSS THE RWY. HE TOLD THE FIRE TRUCK; '...AND THAT BEECHJET DID NOT DECLARE AN EMER.' AS MENTIONED EARLIER; I HAD HEARD OTHER ATC FREQS MENTION WE WERE AN 'EMER ACFT.' I ONLY CORRECTED THEM ONCE; AS HAD OTHER CHORES.