I was wrong about using glass marbles, that is pretty obvious! As Kerry
says, measure from the middle of the track at the top of the playfield
to the upper rail and you will have the radius of the ball.
As for how it worked, a tube amplifier much like used in the Seeburg
Ray-O-Lite games would be my guess. Much like the photo-tubes used in
film projectors of the day for the 'Talkies'. The ball would have to
block the light for X seconds for the timer to do a score increment, so
it would have to travel in line with the tracks to block the light long
enough for the timer to run out. which wouldn't happen if the ball
merely passed through the light beam as it bounced around.
If you can find a solid rubber O-Ring that is the correct length and
diameter, then slit it in half (a jig with a razor blade in the middle
works fine) and secure each side to the walls of the game's playfield. I
do that with regular rubber rings when restoring 30s games that had 1/2
round rubber mupers on the sides - most have used large white rubber
pinball rings cut to size.