LJ35 CREW HAD MAIN GEAR DOOR WARNING LIGHT IN CRUISE.

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APPROX 20 MI INTO THE FLT WHILE CLBING FROM FL200 TO FL230; THE R GEAR UNSAFE LIGHT ILLUMINATED. WHILE CALLED A GEAR UNSAFE LIGHT; IT ACTUALLY INDICATES THAT THE INBOARD GEAR DOORS ARE NOT FULLY CLOSED. WE SLOWED TO BELOW VLO AND CYCLED THE GEAR 3 TIMES. GEAR OPERATED NORMALLY. 3 GREEN; NO RED; WHEN EXTENDED. THE ONLY ANOMALY WAS 1 RED LIGHT ON RETRACTION. NO OTHER INDICATION OF GEAR DOOR OPEN SUCH AS ASSOCIATED NOISE. CONCLUDED WE HAD INDICATION PROB; NOT A GEAR OR GEAR DOOR PROB. AT NO TIME DID WE REQUEST ASSISTANCE OR DECLARE AN EMER; THOUGH WE DID INFORM ATC OF OUR SIT. EARLY ON THE APCH; WE LOWERED THE GEAR WITH NORMAL INDICATIONS; AND LANDED IN LGA WITHOUT INCIDENT. UNBEKNOWNST TO US; THE EMER EQUIP WAS ROLLED. AFTER LNDG; WE CARRIED OUT A THOROUGH POSTFLT; CAREFULLY EXAMINING THE GEAR; GEAR DOORS; THE LATCHES AND MICROSWITCHES. THERE WERE NO VISUAL INDICATIONS OF ANY PROBS. THE ACFT WAS AIRWORTHY; WE HAD HAD AN INDICATION GLITCH WHICH HAD CLRED ITSELF. WE FLEW PART 91; EMPTY; BACK TO TEB (OUR HOME BASE) WITH NO ANOMALIES WHATSOEVER. AS A PRECAUTION; MAINT SWUNG THE GEAR; BUT COULD NOT DUPLICATE THE ERRONEOUS INDICATION. UNFORTUNATELY; ATC MISTOOK A GEAR DOOR INDICATION GLITCH AS BEING A LNDG GEAR EXTENSION PROB. AS A RESULT; THE FAA BECAME INVOLVED; BELIEVING WE HAD DEPARTED LGA WITH AN OPEN; SERIOUS SQUAWK.