As Rolf shows in his schematic snippet (post #8), during the reset cycle there are a set of switches on the player unit that close to supply pulses from a 1A (and also a 4A) motor switch. These pulses are what step the score units back around to zero. On a two-player game, these switches are on the player unit in a switch stack operated by two of the cams. On a four-player game, these switches are on the Z1 and Z2 relays, and the Z1 and Z2 relays themselves are energized by rivets and wipers on the player unit disc.
The runout switch on a score unit opens when the score unit gets to zero. When the runout switch opens, it stops that score unit from stepping any more. In this way, each score unit stops itself when it gets to zero. When all the score units get back to zero, another switch on each score unit closes. These are wired in series, and when all of them are closed, that signals the player unit that it's OK to start moving again, which will complete the reset and start the game at ball 1, player 1.