B737 CREW DIVERTS FOR FUEL FILTER BYPASS LIGHT BUT DOES NOT FOLLOW QRH PROC.

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DURING CRUISE AT FL360 WE EXPERIENCED AN INTERMITTENT #2 ENG OIL FILTER BYPASS LIGHT. WE FOCUSED OUR ATTN ON IT AND WERE NOT CERTAIN OF THE VALIDITY OF THE INDICATION WITH THE SUPPORT OF COMPLETELY NORMAL ENG PARAMETERS AND THE LIGHT BEING UNSTEADY. WE WERE APPROX 110 NM FROM ZZZ. WE NOTIFIED ATC THAT WE WANTED TO DIVERT TO ZZZ WITH A POSSIBLE ENG PROB. WE WERE GIVEN DIRECT ZZZ AND A DSCNT TO A LOWER ALT. WE BEGAN A STEEP DSCNT AND PROCEEDED DIRECTLY TO ZZZ. WE REVIEWED THE QRH AND WERE ANALYZING THE PROB. AT SOME TIME DURING THE DSCNT WITH THE THRUST LEVER AT IDLE; THE LIGHT CAME ON STEADY. AT THAT POINT WE DETERMINED THAT WE WOULD HAVE TO SHUT DOWN THE ENG (AT APPROX FL200 THE LIGHT EXTINGUISHED). WE TESTED THE LIGHT AND FOUND THAT IT WAS WORKING. THE ENG PARAMETERS WERE ALL NORMAL; WITH THE OIL FILTER BYPASS LIGHT EXTINGUISHED; SO WE DECIDED TO CONTINUE TO ZZZ WITHOUT SHUTTING DOWN THE ENG. THE APCH AND LNDG WERE UNEVENTFUL AND THE ACFT WAS GIVEN TO MAINT IN ZZZ. THIS RPT WAS SUBMITTED WITHIN 24 HRS OF BEING NOTIFIED BY CHIEF PLT OF POSSIBLE VIOLATION OF PROCS. DUE TO COMPRESSION OF EVENTS IN A SHORT DISTANCE AND TIME; I SHOULD HAVE IMMEDIATELY FOLLOWED THE QRH AND SHUT DOWN THE ENG.