ACFT EQUIP PROB APPARENT AT RAMP DURING PREFLT. ACFT TAKEN ON FLT REGARDLESS OF LNDG GEAR INDICATOR PROBS.

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ON THE GND AT CMH; WE NOTICED THAT THE 'A' SYS LNDG GEAR GREEN LIGHTS WERE NOT ILLUMINATED. THE SYS WAS WORKING NORMALLY ON OUR LNDG AND TAXI IN. WE NOTICED FURTHER THAT THE 'A' SYS INDICATOR CIRCUIT BREAKER HAD POPPED AND ATTEMPTED TO RESET IT. THE CIRCUIT BREAKER RESET MOMENTARILY AND INDICATED THAT BOTH THE 'A' AND 'B' SYS WERE OPERATING NORMALLY. THE CIRCUIT BREAKER THEN POPPED AGAIN. WE DECIDED TO LEAVE IT OUT FOR THE TIME BEING. I THEN TESTED THE LNDG GEAR INDICATOR LIGHTS AND BOTH SYS FUNCTIONED NORMALLY. ON MY POSTFLT WALK AROUND INSPECTION I HAD NOTICED QUITE A BIT OF WET GRIT ON ALL THE TIRES AND ESPECIALLY THE NOSE GEAR. I BELIEVED THAT THIS WAS THE PROB SINCE ONLY THE 'A' SYS INDICATOR LIGHTS AND INDICATOR CIRCUIT BREAKER WERE OUT. WE DECIDED THAT IT WAS ONLY AN INDICATOR PROB AND THAT IT WAS SAFE TO PROCEED. WHILE ON THE TAXI OUT; I REACHED UP AND RESET THE CIRCUIT BREAKER AND THE SYS SEEMED TO BE NORMAL. ON DEP FROM CMH WITH THE FO FLYING THE ACFT; I CYCLED THE GEAR UP. AS THE GEAR WENT UP; THE 'A' SYS RED LIGHTS DID NOT ILLUMINATE AND THE GREEN 'A' SYS LIGHTS WENT OUT. THE 'B' SYS RED LIGHTS STAYED ON. I THEN RECYCLED THE GEAR TO THE DOWN POS AND GOT 3 GREEN LIGHTS ON THE 'B' SYS ONLY. I NOTICED THAT THE 'A' SYS CIRCUIT BREAKER HAD POPPED AGAIN. I TRIED TO RESET IT; BUT IT WOULD NOT. SO; I LEFT THE GEAR IN THE DOWN POS. AT THAT TIME MY FO SUGGESTED THAT WE RETURN TO CMH. HOWEVER; I DECIDED TO CONTINUE THE FLT SO THAT I COULD TROUBLESHOOT THE PROB AND TO CONTACT MAINT. I THEN TOLD HIM TO FLY THE ACFT AND HANDLE COMS WHILE I RAN THE APPROPRIATE CHKLIST. IT SHOULD BE NOTED THAT WE WERE IN SOLID IFR CONDITIONS AND I THOUGHT THAT THIS WAS THE BEST COURSE OF ACTION. I PROCEEDED WITH THE CHKLIST BUT DID NOT SOLVE THE PROB. I TRIED TO RESET THE CIRCUIT BREAKER; AND ALTHOUGH IT STAYED IN; WE HEARD WHAT SOUNDED LIKE A MOTOR RUNNING CONTINUOUSLY AND DECIDED TO PULL THE CIRCUIT BREAKER AND LEAVE IT OUT. WE HAD THE 'B' SYS GREEN LIGHTS ILLUMINATED AND NO UNSAFE GEAR INDICATIONS. I TALKED TO MAINT OVER THE RADIO AND THEY AGREED THAT IT WAS PROBABLY AN INDICATOR PROB. UPON TALKING TO CVG APCH CTL; I ADVISED THEM OF OUR SIT AND REQUESTED CFR EQUIP TO STANDBY AS A PRECAUTION. I CALLED OUR 'EXCEPTIONS' FREQ AND TOLD THEM TO HAVE 'RED COATS' (CSR'S) AT THE GATE; IF POSSIBLE. I THEN SPOKE TO OUR PAX VIA THE INTERCOM TO INFORM THEM OF THE SIT. FINALLY; I SPOKE WITH OUR FLT ATTENDANT AND TOLD HER WHAT WAS GOING ON. THE APCH CTLR ASKED US IF WE WISHED TO DO A TWR 'FLY- BY' TO HAVE THEM CHK THE LNDG GEAR FOR US. HOWEVER; MY FO AND I AGREED THAT THIS WOULD BE UNNECESSARY SINCE WE WERE SURE THAT IT WAS ONLY AN INDICATOR PROB AND THAT WITH THE WX BEING 400 FT OVCST AND 2 1/4 MI VISIBILITY THAT IT WOULD BE A RATHER FRIVOLOUS MANEUVER THAT MIGHT UPSET THE PAX UNNECESSARILY. WE THEN SHOT THE ILS RWY 36R APCH AT CVG AND LANDED WITHOUT INCIDENT. SEVERAL CFR VEHICLES FOLLOWED US TO OUR GATE AS IS STANDARD PROC. THE PAX WERE DEPLANED WITH CSR'S AVAILABLE WITHOUT ANY PROB. UPON REQUEST OF MAINT; WE THEN TAXIED THE ACFT TO THE HANGAR. AT THE HANGAR I TALKED TO A MAINT SUPVR WHO TOLD ME THAT A SIMILAR PROB HAD ARISEN ON ANOTHER ACFT AND THAT IT WAS EITHER A LOOSE CANNON PLUG OR A RELAY BOX THAT PROBABLY WAS THE SOURCE OF PROB.