If it isn't a magnetar, my money's on it being a binary object like a quasar orbiting something massive. The massive object will be stabilising the quasar's spin in much the same way our Moon stabilises Earth's axis somewhat, but the beam of this object won't cross Earth unless it's at the right point in its orbit.

One might expect a 22 minute orbit around a massive object to have decayed a bit over 35 years (that would definitely be something to test for), but there's nothing that says the orbit or rotation period is 22 minutes, only that there's a resonance of 22 minutes coming from some interaction or another.