Actually, the way they worked was this:
When the table descended to set a fresh rack of ten pins, it would stop in the down position.
Meanwhile, sticking up from the middle of the ball return was a console. This console had 13 positions on it from top to bottom. The top six positions represented the six players you could have listed on the left lane, 1 thru 6, on the scoresheet. The bottom six positions represented the six players you could have listed on the right lane, 1 thru 6, on the scoresheet. Then there was also a practice position in the middle.
Before the pinsetter table would raise, you'd first have to press the button on the slider, either on the left side of the console (for when you're bowling on the left lane) or on the right side of the console (for when you're bowling on the right lane). You'd press the button down and hold it while sliding the thing into the position where your name was on the scoresheet. So if I was the #2 bowler on the left lane, I'd take the lever on the lane I was about to bowl on and slide it up to the top #2 position (the top group was for the bowlers listed on the left lane). When I let go, the slider would lock into position and the pinsetter table would raise, revealing the fresh set of pins.
After that, everything worked pretty much the way you'd expect a Brunswick A2 pinsetter to work, with one exception: Following the second ball in a frame, the table would descend, just as it would after the first ball. But this time, it wouldn't pick up any remaining pins. But it would COUNT the number of pins left standing. This is how the pin count got relayed to the scoring system.
The actual projectors which shot the image of the scoresheets up to the screens above the approaches were 4 wide. In other words, each one handled the scoring for 4 lanes and were positioned behind the bowlers' settee area. These huge projectors each had four printers, one for each lane. You'd slip the little scoresheets in. There were tractor holes on either side of the paper, which was a little smaller than a recap sheet, and had a coating of wax on the back. So when the printer hammered the letters/numbers on to the scoresheets, the wax would stick to the glass, creating the image of the numbers on screen. You'd have to use a kleenex and some cleaning solution to wipe the glass clean after each game of league, or after all the scoresheet lines were full during open play.
It was a pretty slick system for its time. The ones seen in this video at Golden Triangle Lanes in Irving, TX were installed this way. Golden Triangle was the sister house of Forum Bowl in Grand Prairie, TX about 10 miles away. Forum Bowl played host for many years to the PBA's Quaker State Open (it was the house with the chandeliers hanging from the ceiling all throughout the center -- they're gone now, although Forum Bowl is still very much open and successful, and was one of the host centers to last summer's Junior Gold Championships). And Golden Triangle Lanes played host to the second Great and Greatest Tournament, which basically was the pilot for what would become the Senior Tour. Anyway, these Brunswick Astroline scoring systems were installed when the two centers were built, both in the early '70s. Other centers around the country had their pinsetters retrofitted by Brunswick to work with these systems. But they were originally installed this way at Forum Bowl and Golden Triangle Lanes.
AMF's MagicScore system would follow a few years later. That was the first paperless system. Stashed away somewhere around here, I probably still have some old scoresheets from this Brunswick Astroline Scoring System.