I do not believe there is any rule about a 60 min cutoff at JFK. At least the TSA does not seem to care.

FWIW, in 2019 I offered my J seat on an overbooked flight out of JFK and they asked me to wait next to the check-in counter until the flight was closed. At around 45 mins prior to departure, they informed my that there were no-shows and my seat would no longer be required and I could continue. I made it through security barely before the departure time and found to my relief they were still boarding.

Here is another data point that might be helpful. On my return from LAX earlier this month, I was selected for 'special screening' - you get to know this when your BP shows 'SSSS' printed at the bottom. The special screening was conducted in a designated secluded area, away from the main security lines. It took them around 15 minutes to gather the folks who could do the special screening. Then one of the machines gave an alert code and that required another 2 rounds of 'pat downs' by team leaders, multiple explosive scans, and an inspection of all my carry-ons by an explosive expert. They figured it could be an incorrectly calibrated machine that caused the alert. Finally, when they let me go it was over 75 minutes since I had got into the line for security.

So even though the 60 minute cutoff may not be enforced at JFK by TSA, other events could delay you significantly that could cause you to miss your flight.