Neutrons pass through rock quite well.
Reactors are basically just giant neutron transmitters, by modulating reactor output you also modulate their neutron output.
Flipping a magnet definitely won't penetrate a shield better than neutrons, in fact because of Gauss' law it probably won't penetrate at all.
Gauss’ law is for the electric field. The magnetic field is very difficult to block and we have incredibly sensitive magnetometers (probably ones that can detect magnetic anomalies of a submarine from space)
In fact, thats pretty much how deep submarine communication works very low frequency fields. Thats why I proposed a magnet: a basically static field that cant be blocked.
Is my proposal practical? Well, typically not. But if the alternative is neutron communication, I dont see why not.
[1] to a first approx think of thermalizing as momentum exchange upon collision. If you’re similar in mass to the colliding mass you’ll exchange more momentum. Assuming rock is mostly silicon, w/ a mass 28 times larger than a neutron. And there’s at least a km of rock above miners.
[2] throttle a reactor to modulate neutron? Oh boy!
EDIT: actually the crust is mostly oxygen, atomic mass 16. That only strengthens my argument.
https://en.wikipedia.org/wiki/Gauss%27s_law_for_magnetism
Flipping a dipole is literally just radio.
How do you think nuclear reactors are controlled? Nuclear reactors can vary their power output at a rate of tens or even hundreds of MW/minute. While it takes special designs to throttle at high enough speeds for load following, to send a signal you only need to change the power output enough to be detectable by a neutron detector, which need only be slightly greater than the variation due to random noise.