ALL,
>What are the mental tricks old beekeepers use to find queens?
 How much of queen finding is simply determination to keep staring
>at the side of a frame until she is spotted? What kinds of cues do the
>other bees give to the queen's location?
As with every other beekeeper I have ever met, I have trouble finding the
queen at times also.
As far as clues-- look on those frames that have fresh (or any age) eggs.
Although she is not always there, it is a good place to start, since she
has been there recently.  She is infrequently found on the outer frames
that contain only honey (I look there last).  If the bees have not been
disturbed too badly, there may be a "daisy" -- the queen in the center of a
group of workers all of which are facing her.
Examine the frames as well as you can, one by one.  If you cannot find her,
put everything back, and GIVE UP.  It is seldom important enough for me to
spent 45 minutes trying to find her.  I understand that if one is
requeening, the old queen must be found, and in that circumstance, I would
do one of two things.  After a few minutes of looking, I'd put the hive
back together and take a walk for a few minutes ( or check other hives
etc)come back to it after half an hour or so, and start all over again.  If
still unsuccessful, (and this is the second thing) I would put an excluder
between the brood boxes and come back in a day or three.  Look for eggs to
determine which box of the brood chambers she is in, and begin the search.
This time there would be only half the number of brood boxes to search.
I know this requires an additional trip to the yard, time and distance
would determine whether it is more worthwhile to continue to search on the
first trip, or come back later.
Most of the beekeepers I know have at one time or another just plain given
up on finding the queen.  It seems that more often than not the next time
they look into the same hive (a few days or a couple weeks or more later),
it is almost like she has a signal lamp flashing and she is spotted almost
immediately upon opening the hive.  Go figure.
Those GOLDEN Italian queens are much easier to find( and prettier also).
But even they can be elusive.
Take any opportunities you can to help other beekeepers to find queens ( or
assist in any other beework).  This will help you develop an 'eye' for
finding the queen ( although as I said before, there will be times when she
is just nowhere to be found).
Good luck!!
Bill