RAT5 :
There was no chance of collision
Then you will never get an RA.
The collision geographical model is very complex ,not many people really understand it 100% ( me included) but when TCAS works normally, you need to be on collision course to get an RA. In your JFK case, if you follow someone slightly slower it will just be a long TA...until you get very close of course, or below 1000ft AGL.