ACR FLC INTERRUPTED DEP CLB BECAUSE A FALSE TCASII TFC ALERT.

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UNEVENTFUL TKOF AND DEP OUT OF JFK ATA. HDG 090 AND CLBING OUT OF 6000 FT FOR 9000 FT; I NOTICED A TARGET ON TCASII. THE TARGET WAS PAINTED DIRECTLY ON TOP OF US INDICATING AN ALTDEV OF 0 FT; AND REMAINED THAT WAY EVEN AS WE CONTINUED TO CLB. AT THIS POINT I NOTICED THAT TCASII WAS IN THE 'TA MODE'; SO I SWITCHED IT INTO THE 'AUTO MODE' (NORMAL COMPANY PROC CALLS FOR TCASII IN AUTO FOR TKOFS. APPARENTLY THE CAPT PREFERRED TA MODE ON TKOFS AND HAD SWITCHED TCASII TO SUCH WITHOUT INFORMING ME. THIS WAS OUR FIRST FLT TOGETHER AND WE WERE RUSHED BECAUSE OF A LATE DEP; SO WE DID NOT HAVE TIME TO TALK ABOUT THE PARTICULARS). ANYHOW; MY ACTION OF PUTTING TCASII IN AUTO SIMPLY CONTINUED TO CONFUSE THE SITUATION. NOW TCASII WAS GIVING US TFC ALERTS AND VERBAL COMMANDS TO LEVEL THE ACFT. IT WAS VMC; AND NEITHER THE CAPT NOR I COULD SEE ANY TFC. AT THIS POINT THE CAPT (THE PF) LEVELED THE ACFT WHILE I INFORMED ATC OF THE TCASII ALERT AND ASKED IF THERE WAS ANY TFC IN OUR NEAR VICINITY. ATC SAID THE CLOSEST TFC WAS 3 O'CLOCK AND 6 MI AND ASKED IF WE SAW THIS ON TCASII. WE DID NOT. AFTER WE LEVELED OFF; THIS TARGET REMAINED AT A 0 FT ALTDEV WITH TCASII NOW GIVING US DSND INSTRUCTION. AT THIS POINT THE CAPT AND I BOTH REALIZED THAT THIS TARGET WAS INVALID AND IGNORED FURTHER TCASII ALERTS. A FEW SECONDS LATER THE PHANTOM TARGET DISAPPEARED FROM THE SCREEN. THE FLT FROM THIS POINT WAS UNEVENTFUL; WITH TCASII WORKING NORMALLY. TCASII NEVER INITIALLY GAVE US A TA FOR THE TARGET; AS IT SHOULD IN THE TA MODE. THIS TARGET SIMPLY APPEARED WITHOUT ANY INITIAL WARNING.