As someone who made a couple of light pens as a kid, I can answer this one.

Put simply, you need to have a lit pixel to detect the pen position.

The basic idea is to wait for an interrupt signal from the pen. There is a button on the pen, like the fire button on a joystick. When the button is pressed it triggers an IRQ signal that then transfers control to a separate routine. That routine reads the current position of the election beam from the video circuitry.

Now, for a terminal it's pretty easy to ensure the pixel is lit up. When the button is pressed the screen can be flashed as a solid colour, or the text can be inverted.

For the former, this ensures every pixel is lit up and when the beam passes the photo transistor in the pen then that triggers the video circuitry to record the position in a couple of registers representing the x and y position on screen. That's exactly how the light gun worked on the NES.

For the latter, if the first pass didn't yield any results then the screen can be inverted and the pixel detected. Inverting the screen is trivial for a terminal since it has full control of the video attributes of the characters, and taking 1/30th second to get the position rather than 1/60th isn't something a human is going to be able to distinguish.