I have six beacons. I would expect all beams to stay activated while looked in the direction of it from any angle. And they had until I updated and changed the glass.
However since addition of stained glass to colour the beams, the beam disappears past a certain point.
The further away the more of the beacon beam you can see before it disappears as you move your mouse up toward the sky.
But right next to the beam you can move up, maybe 10°.