Whether it collapses 60, 120, or a thousand times a second when
running is not relevant, because when the fan is running, both wires
are connected to the GFCI. With power to the fan routed through a
single-pole switch so that only the hot conductor is opened by the
switch, only *one* wire is connected to the GFCI, thus making it
possible for the collapsing field to cause imbalanced hot and
neutral currents at the GFCI.

With only "one" wire connected to the GFI there is no difference of
potential either. It kind of makes induced currents impossible too,
but run with it.

Maybe you ought to spend a little more time thinking about that...

Want to bet on the double pole switch?

Sure.

I have to admit, I'm a little skeptical about the double-pole switch.
Whether resistive or inductive, how can you have current flow unless the
circuit is completed? Open the hot wire and current shouldn't flow through
the neutral either, unless there really was a fault in the wiring
somewhere? I was an electronic tech MANY years ago, so maybe I've just been
away from this stuff too long.

In any case, my own attempts at solving the problem have failed, so I'm
willing to give it a try. I bought a double-pole switch yesterday ($9) and
plan to install it in the next day or two. Unfortunately, due to the
erratic nature of the problem, I may not know for a month or more whether
it solved the tripping problem. But, if it does trip again, at least I can
rule out the switch once and for all.

Thanks for the feedback!

Anthony