Why is this a different "sense" organ? Because it uses the sense of "touch"? Is a handheld compass also an "on-body" circuit?
Evolutionarily, we at least have the vestiges of a "sense" of magnetic bearing - our brains contain tiny magnetite
crystals, similar to (though much smaller and fewer) those found in birds, which do function to give them a
sense of absolute direction. So whether or not we can reactivate that sense, we at least (probably) have the underlying
wiring necessary to use it.
As for the cross-modality of this... Judging by TFA and other similar experiements about which
I've read, I would say that we can indeed awaken that sense by providing an alternate means of
inputting the relevant data (in this case, via touch).
But to compare this to looking at a normal compass, the biggest difference, I would say, comes from it
providing constant and passive feedback about the local magnetic environment. Looking at a
compass will indeed tell you which way to call "North", but you don't "experience" it as anything but a name
for the way the needle points. If instead, you always had an accurate sense of North, I would expect
it to affect you much more strongly - Your proprioception would suddenly include an absolute orientation
rather than merely relative positioning.