A B737-300 WAS OPERATED FOR 3 LEGS WITH AN INTERMITTENT L ENG OIL FILTER BYPASS LIGHT. ON 4TH LEG; DECLARED AN EMER AND DIVERTED.

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ON THE INITIAL START OF THE #1 ENG OF ACFT X (-200 SERIES) THE #1 OIL FILTER BYPASS LIGHT ILLUMINATED AS HAS BEEN CONSIDERED SOMEWHAT NORMAL FOR THE FIRST START OF THE DAY WITH AN OUTSIDE AIR TEMP OF 10 DEGS C. WE LET THE ENG IDLE WHILE ACCOMPLISHING THE AFTER START CHKLIST. THE LIGHT EXTINGUISHED AFTER ABOUT 2 MINS. DURING TKOF ROLL; THE SAME LIGHT RE-ILLUMINATED AFTER TKOF THRUST WAS APPLIED. I ELECTED TO DISREGARD IT FOR A FEW SECONDS TO SEE IF IT WOULD AGAIN GO OUT; WHICH IT DID -- PROBABLY AT ABOUT 80 KTS OR SLIGHTLY BELOW. WE CONTINUED THE TKOF AND FLEW UNEVENTFULLY TO ZZZ1 WITH NO OTHER INDICATIONS. TKOF FROM ZZZ1 WAS ALSO WITHOUT ANY MORE PROBS WITH THIS LIGHT. ON FINAL APCH INTO ZZZ; THE LIGHT RE-ILLUMINATED. SINCE I CONSIDERED THIS A CRITICAL PHASE OF FLT; WE CONTINUED OUR APCH WITH NORMAL CONFIGN AND DISCUSSED WHAT WE WOULD DO IF THE ENG SHOULD QUIT OR NEED TO BE PULLED BACK. THE LIGHT AGAIN WENT OUT AFTER A SHORT TIME AND THE LNDG WAS MADE. ON THE GND AT ZZZ I TALKED TO MAINT DUTY CTL AND DISCUSSED WHAT HAD BEEN HAPPENING. WE BOTH AGREED THAT SOMETHING WAS GOING AWRY WITH THE OIL FILTER OR ITS FILTER BYPASS LIGHT SYS AND FELT THAT WE COULD CONTINUE BACK TO ZZZ2 WITH THE SINGLE STOP AT ZZZ1. THE THOUGHT WAS TO GET IT BACK TO ZZZ2 AND HAVE IT CHKED THERE. ON DEP FROM ZZZ; THE LIGHT AGAIN ILLUMINATED SHORTLY AFTER TKOF. WE CLBED TO 1000 FT; RETRACTED THE FLAPS; AND WENT THROUGH THE QRH PROC FOR A FILTER BYPASS PROB. AFTER RETARDING THE LEVER TO PARTIAL PWR; THE LIGHT EXTINGUISHED. WE CONTINUED THE CLB AND BEGAN TO EVALUATE THE THOUGHTS OF PROCEEDING TO ZZZ1 OR RETURNING TO ZZZ. AS WE CLBED WE HAD TO CONTINUE REDUCING THRUST TO KEEP THE LIGHT EXTINGUISHED AND AT APPROX 10000 FT; WITH THE THRUST LEVER AT IDLE AND THE LIGHT ILLUMINATED CONTINUOUSLY; WE DECIDED TO RETURN TO ZZZ. THE QRH PROC CALLS FOR SHUTTING THE ENG DOWN IF THE LIGHT STAYS ILLUMINATED AND THIS IS WHAT MY INITIAL INTENTION WAS. THE FO WAS FLYING THE ACFT AND I WAS DOING THE CHKLIST. AFTER STARTING THE APU AND WHILE ON A COURSE BACK TO ZZZ; I DECIDED THAT I WOULD PREFER TO OPERATE THE ENG AT IDLE UNTIL I SAW SOME OTHER SIGN OF AN ENG PROB SUCH AS HIGH OIL TEMP; LOW OIL PRESSURE; OR A VIBRATION. MY THOUGHTS WERE THAT THIS MIGHT BE JUST AN INDICATION PROB AND I MIGHT BE SHUTTING DOWN A PERFECTLY GOOD ENG. WE USED SINGLE ENG PROCS; DECLARED AN EMER; AND LANDED UNEVENTFULLY AT ZZZ. IN RETROSPECT; I HAVE LEARNED THAT THE PROB WAS CAUSED BY METAL IN THE OIL FILTER. BECAUSE OF THE EARLIER MOMENTARY ILLUMINATIONS OF THIS LIGHT I DID NOT HAVE CONFIDENCE THAT IT WAS TELLING THE TRUTH. IT WAS. I AM NOT SURE IF THE LIGHT ILLUMINATING AFTER ENG START IN ZZZ2 WAS CAUSED BY METAL OR SUPPOSEDLY 'COLD OIL.' THE SAME WITH ILLUMINATION DURING THE EARLY TKOF ROLL AT ZZZ2. THE ALTERING OF THE QRH PROC ON MY PART WAS DONE UNDER CAPT'S EMER AUTH.