B737-300 CREW HAD ERRATIC LOC SIGNALS ON ILS RWY 13 AND RWY 7 AT JAX. A PAX WAS USING A 'PALM PILOT' AT THE TIME.

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WE WERE AT 2000 FT MSL ON A HDG CLRED TO MAINTAIN 2000 FT TILL ESTABLISHED AND CLRED FOR THE ILS RWY 13 AT JAX. THE LOC CAME ALIVE AND THE FO WHO WAS FLYING BEGAN A DSCNT TO 1700 FT WHICH WAS THE GIA. JUST AFTER BEGINNING THE DSCNT; THE LOC BEGAN TO PING FROM SIDE TO SIDE ON BOTH CAPT AND FO'S INSTS. WE INFORMED JAX APCH OF THE PROB; CLBED BACK TO 2000 FT AND WERE GIVEN ANOTHER VECTOR AS WE HAD GONE THROUGH THE COURSE. THERE WERE NO FLAGS AND THE IDENT WAS GOOD. APCH THEN SAID IF WE CONTINUED TO HAVE A PROB WITH THE ILS; WE WOULD BE GIVEN A SURVEILLANCE TO RWY 7. I ASKED IF ANYONE WAS IN THE CLR ZONE AND WAS INFORMED THAT THERE WAS NOT. ADDITIONALLY; THE ACFT PRECEDING US AND BEHIND US HAD NO LOC PROBS. WE CONTINUED TO HAVE DIFFICULTY WITH THE LOC AND ENDED UP FLYING THE SURVEILLANCE TO RWY 7. THE ILS SEEMED TO OPERATE FINE ON THE GND AND SINCE WE HAD NO PROBS WITH IT EARLIER; I THOUGHT PERHAPS SOMEONE HAD USED SOME ELECTRONIC EQUIP IN THE CABIN DURING OUR APCH. I CHKED WITH THE FLT ATTENDANTS AND; IN FACT; A GUY HAD OPERATED A PALM PILOT OF SOME SORT DURING THE APCH. WE WERE UNABLE TO TALK TO THE PAX BECAUSE HE HAD ALREADY LEFT THE ACFT BY THE TIME WE TALKED TO THE FLT ATTENDANTS. I ASSUMED THAT WAS THE PROB AND ADVISED THE CREW WHO TOOK THE ACFT AT JAX WHAT HAD OCCURRED. I DID NOT WRITE UP THE OCCURRENCE IN THE LOGBOOK. AFTER FURTHER REFLECTION; I PROBABLY SHOULD HAVE BECAUSE THERE IS NO WAY I CAN PROVE THE PALM PILOT WAS THE CAUSE.