Hmm... The second idea would also work with standard vacuum tubes that
have more than one anode. Or even two or more electrodes of any type that
is separated from each other by a small amout, that can be used as anodes.
The magnetic field would shift the electron flow from one electrode to the
other. I'll have to do some experiments on that subject.

I have looked at over a 100 different tube types that I have on had. Ranging
from the 4 pin 01A to a bunch of different compactatrons. I haven't found
one with the correct electrode structure to do a good job at detecting
polarity and intensity. The only two that I found, that would possibly make
a good intensity detector is the 6AV6, and the 6JH8.

You would have to have a tube with two anodes about the same distance from
the cathode, with both anodes on the same side of the cathode.

(ie) the electrons leave the cathode in one direction, headed for the group
of two electrodes. The amount of current arriving at each electrode will be
a function of the magnetic field along the path. The magnetic field will
curve the path to one electrode, or the other, depending on magnetic
polarity. And the current distribution between the two electrodes would
indicate intensity.

The only thing that draws even close to that is a cathode ray tube with
deflection plates. Operate it with the focus out of adjustment enough that
the deflection plates are pulling a measurable current. Then the current
distribution between the plates will depend on how the magnetic field is
shifting the electron beam.