But what they radiate seems to be all over the map. Sometimes they radiate gammas but not radio, sometimes radio but not gammas, sometimes both. Why? Maybe it has to do with which way the star is pointed relative to us.
based on these observations, Geminga’s magnetic poles appear to be oriented at the top and bottom of the neutron star from our point of view, which also align with its spin poles. Because these areas are where a pulsar’s radio emission should originate, it makes sense that no radio waves are detected. The pulsar’s gamma rays, however, are created over a larger area at higher altitudes, causing them to sweep out over a larger area of the sky and making them detectable from Earth.
It makes sense. Verifying that would be kind of hard--we'd have to have a clear idea of how far from the rotational axis the magnetic poles point, and then try to correlate that with the ratio of gamma to radio. But I've no idea how to measure that angle. You could get some notion of the direction of the axis of rotation from the jets of stuff shot away from it (you'd measure the doppler shifts of each of the two lobes to try to pin down their speed and direction), but measuring the magnetic field direction sounds hard. Polarization of light would be going this way and that with the moving field, and I'm not sure you could tell that from randomness.