Good point, Terminal 4 security is a crapshoot. Sometimes it’s packed, sometimes it’s empty. But if you have Clear/Precheck it’s a breeze
EK does not have their own TSA line.
That comment about it being a crapshoot is for real. Ive flown from T4 on both the morning and evening departures and the TSA Pre-Check and Clear lines both get shut down randomly at the whim of the TSA on the day. There is no consistency nor predictability to that madness. It seems to be worst at night, where I've had to be escorted through the endless NO- Precheck/NO-Clear security scrum by EK handling agent in spite of arriving 90 minutes before departure. I can't recall ever being there at night when the Pre-check or Clear was operational, though it is the time when it is most sorely needed. I did use an active Pre-check lane in the morning once, when the lack of crowding made it much less of an advantage.
TL/DR - Don't count on Precheck / Clear being available at JFK T4 when it is most needed. It seems to be closed at the busy times and open at the un-busy times.