AN SMA LOST IT'S EXTERNAL LIGHTS AT NIGHT IN THE TFC PATTERN.

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I WAS MAKING 3 FUEL STOP LNDGS TO QUALIFY UNDER FAR 61.57 (A); RECENT FLT EXPERIENCE (NIGHT). I HAD AN INSTRUCTOR FLY WITH ME. THE ACFT WAS THOROUGHLY PREFLTED. ALL LIGHTS; INCLUDING ANTI-COLLISION STROBES; POS; AND INTERIOR LIGHTS WERE CLRED AND FOUND TO BE WORKING PRIOR TO ENG START. I REQUESTED CLOSED TFC FOR 3 STOP AND GO LNDGS. TWR DIRECTED US TO MAKE L TFC FOR RWY 32. WHILE TURNING BASE FOR THE SECOND LNDG; TWR ADVISED THAT HE COULD NOT SEE OUR POS LIGHTS. WE RECYCLED THE SWITCH; CHKED THE CIRCUIT BREAKERS AND LANDED. WE STOPPED ON THE RWY AND AGAIN CHKED POS LIGHT SWITCH. THE POS LIGHTS ARE NOT VISIBLE FROM THE COCKPIT. I WAS UNCERTAIN WHETHER THE LIGHTS WERE ON; BUT THE TWR CTLR SAID; 'ARE YOU GOING TO ROLL?' ASSUMING THAT HE SAW THE LIGHTS I REPLIED; 'YES' AND APPLIED FULL PWR FOR THE TKOF. THE THIRD LNDG WAS COMPLETED AND WE CLRED THE RWY. AFTER WE SHUT DOWN; SECURITY APCHED THE ACFT AND ASKED FOR MY LICENSE AND TO SPEAK WITH A CTLR (GND) ON HIS MOBILE RADIO. THE CTLR STATED THAT AFTER CLRING US TO ALPHA AREA AND HEARING OUR ACKNOWLEDGEMENT; OUR ANTI COLLISION STROBES WENT OFF AND HE WAS UNABLE TO CONTACT US ON 121.6 AND THAT THERE WAS A POSSIBLE CONFLICT WITH ANOTHER ACFT ON THE GND. I TOLD HIM OUR RADIOS REMAINED TUNED TO 121.6 UNTIL WE SHUT DOWN; BUT WE DID NOT HEAR HIM. IT APPEARS THERE WAS AN ELECTRICAL PROB WITH THE ACFT. WE SMELLED SOMETHING BURNING WHILE IN FLT; BUT ATTRIBUTED IT TO THE HEATER; AS THE SMELL DISAPPEARED SHORTLY. THE OWNER/OPERATOR OF THE RENTAL ACFT CORROBORATED THAT THERE HAD BEEN AN ELECTRICAL PROB.