B737-700 CREW HAD BOTH THE LNDG GEAR DOWN GREEN LIGHTS AND THE UNSAFE GEAR RED LIGHTS ILLUMINATE ON APCH TO EWR; ELECTING A GAR TO TROUBLESHOOT THE PROB.

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I WAS PF AND CALLED FOR GEAR DOWN DURING NORMAL ILS APCH TO RWY 22L AT EWR. GEAR INDICATED 3 GREEN AND 3 RED LIGHTS. OVERHEAD GEAR INDICATORS ON THIS B737-700 INDICATED 3 GREEN. QUICK DISCUSSION ABOUT JUST CYCLING GEAR; BUT WE DECIDED TO GO AROUND; RUN APPROPRIATE CHKLIST AND TAKE OUR TIME TO FIGURE IT OUT. ACCOMPLISHED GAR; CLBED TO 5000 FT AS DIRECTED AND WERE VECTORED BACK AROUND FOR ILS. AS WE GOT OUT THE QRH; WHEN MAKING SURE THE GEAR HANDLE WAS ACTUALLY ALL THE WAY DOWN; THE RED LIGHTS WENT OUT TO SHOW NOW ONLY 3 GREEN. THE GEAR HANDLE WAS JUST NOT ALL THE WAY DOWN; SOMEWHAT LOOSE; AND ONLY MOVED 1/8 OF AN INCH WHEN WE PRESSED ON IT. NOW WITH A NORMAL INDICATION; WE DECIDED TO NOT DECLARE AN EMER; CONTINUE AROUND WITH THE GEAR DOWN; AND COMPLETE THE APCH. NORMAL CHKLIST WERE RUN; EVERYONE WAS NOTIFIED; AND AN UNEVENTFUL LNDG WAS MADE. NOTHING ELSE ABNORMAL OCCURRED AND THE FLT BLOCKED IN AS NORMAL. SUPPLEMENTAL INFO FROM ACN 622288: DURING GEAR EXTENSION ON APCH INTO EWR WE NOTICED THAT THE 3 GEAR UNSAFE LIGHTS REMAINED ILLUMINATED. ALSO THOUGH; ALL 6 (UPPER AND LOWER) GEAR DOWN AND LOCKED LIGHTS WERE ALSO ILLUMINATED. I WANTED TO CYCLE THE GEAR; BUT MY FO DIDN'T AND I BRIEFLY DISCUSSED MY AWARENESS OF THE MEMO REGARDING THE DANGERS OF RECYCLING GEAR. HE WAS STILL UNCOMFORTABLE; SO WE TOOK THE MOST CONSERVATIVE OPINION AND ACCOMPLISHED A GAR. I PULLED OUT THE QRH TOO; AND WAS UNABLE TO LOCATE A SPECIFIC PROC FOR THIS CONDITION. ATC ASKED US ABOUT THE NATURE OF THE PROB. AFTER TELLING ATC; A PLT SID TO 'CHK THE HANDLE' ON THE FREQ. AS SOON AS I HEARD THIS; I REALIZED IMMEDIATELY THAT THE HANDLE PROBABLY WASN'T COMPLETELY STOWED. WE PUSHED THE HANDLE IN ABOUT 1/8 OF AN INCH AND THE RED LIGHTS DISAPPEARED. WE ADVISED ATC THAT THE PROB WAS RESOLVED AND THAT NO FURTHER ASSISTANCE WAS NECESSARY. CYCLING THE GEAR ON APCH VERY WELL MAY HAVE RECTIFIED THE PROB; HOWEVER; I DIDN'T FEEL THAT AN EXTENDED DEBATE OVER WHETHER OR NOT TO CYCLE THE GEAR WAS APPROPRIATE DURING THIS PHASE OF FLT. I FEEL COMFORTABLE WITH THE DECISION TO GO AROUND AND TAKE THE MORE CONSERVATIVE RTE; EVEN THOUGH IT PROBABLY WASN'T THE MOST EXPEDITIOUS. MY THANKS TO THE PLT ON THE FREQ. HE OBVIOUSLY HAD SEEN THIS PROB BEFORE. NEEDLESS TO SAY I WON'T FORGET TO CHK THAT THE GEAR HANDLE IS NOT ONLY DOWN; BUT ALSO PUSHED IN FULLY; IF I SEE THIS HAPPEN AGAIN.