writes:

Quite a few amounts to a very small number scattered about the globe
and ATC has no phone list of such simulators, much less a list sorted
by aircraft type, and the numbers of people qualified to run such a
simulator.

I'm reminded of a cartoon in which someone picks up a phone, dials a number,
and hears "U.S. Government, may I help you?"

ATC doesn't need phone lists of simulators or airline pilots or anything of
the kind.

Even I can find an instructor pilot in a few minutes with a few calls. Air
traffic control facilities can do the same thing, only much faster and much
more easily.