They have transponders. But military airplanes can and sometimes do turn them off. When airplanes broadcast signals they can be detected. The military sometimes wishes to avoid this.
One of the article updates quotes from a Washington Post story:
> "The jet’s transponder, which usually helps locate the aircraft, was not working “for some reason that we haven’t yet determined,” said Jeremy Huggins, a spokesman at Joint Base Charleston. “So that’s why we put out the public request for help.”
It could activate after ejection, certain acceleration pattern (i.e. crash) or could start broadcasting only after receiving very specific signal (one-time code) on a specific frequency. There are probably plenty more options, it doesn't seem like a hard problem from engineering standpoint.
Civilian aircraft, even 2 seaters, have had ELTs for decades. They are being replaced with better systems, but they were designed to do just that: broadcast a signal on a specific frequency after a crash.
Doubtful you want to broadcast the position of the latest generation stealth fighter, however.
As mentioned, it can be silent until receiving specific signal. It can be single frequency it can be multiple, but if it's specific string of bytes or specific timing it's practically impossible to brute force when it's long enough, and when looking for the plane you can broadcast it with high intensity because it is only single use.
> "The jet’s transponder, which usually helps locate the aircraft, was not working “for some reason that we haven’t yet determined,” said Jeremy Huggins, a spokesman at Joint Base Charleston. “So that’s why we put out the public request for help.”