A B737 ABORTED TKOF AT 60 KTS WITH AN ENG CTL LIGHT ON. DISPATCHER CONTACTED MAINT CTL AND RELAYED INSTRUCTIONS TO CREW.

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IT HAS RECENTLY COME TO MY ATTN THAT THERE IS SOME DISCREPANCY AS TO THE DIALOG AND COURSE OF ACTION THAT TOOK PLACE REGARDING A MECHANICAL ISSUE ON FLT XXX-YYY. I RECEIVED A CALL FROM XXX OPS REQUESTING RADIO PATCH TO FLT NUMBER. CAPT STATED THAT WHEN THEY TOOK THE ACTIVE AND THROTTLED UP; THEY GOT THE #1 ENG CTL LIGHT ON STEADY. THEY HAD TAXIED OFF THE RWY AND ASKED FOR GUIDANCE. AFTER ADVISING MAINT CTL OF THE SIT AS I UNDERSTOOD IT FROM CAPT; I RELAYED MESSAGE TO SHUT DOWN ENG AND RESTART. IF LIGHT DID NOT EXTINGUISH; INSTRUCTIONS WERE TO RETURN TO GATE. AFTER A FEW MINS; CAPT CONFIRMED LIGHT OUT. HE ASKED IF ANYTHING NEEDED TO BE WRITTEN UP. AGAIN; REFED MAINT CTL WHOSE ANSWER WAS NO. LATER ON; I READ AN ACARS VERY CASUAL MSG REGARDING WX DEV AND THANKS FOR HELP; THEN ANOTHER ACARS AS TO WHETHER OR NOT THEY NEEDED MAINT IN YYY. I CONFIRMED NO ADDITIONAL PROBS AND THEN SET UP THROUGH MAINT CTL FOR A MECH TO MEET ACFT ON ARR AND PERFORM BITE CHK. AT NO TIME DURING ANY CONVERSATION (VIA RADIO OR ACARS) WAS I MADE AWARE OF THE ABORTED TKOF AT 60 KTS OR THE CAPT'S CONCERN REGARDING LOGBOOK ENTRY.