It's hard to say without a schematic. Generally all score reels have two circuits that drive them. One is used only during reset to return the score reels to zero. The other is used only during the game to increment the score reels one step for each pulse. Here's an example from Flying Chariots:
Flying Chariots score reels (resized).jpg
It shows the circuits for both 100 point score reels in a two player game. The lower circuit into each score reel is used only during a game and is driven by switches on the Q/100 Point relay and the P/2nd Player relay. The Q relay switch closes whenever 100 points have been scored and the P relay switch determines which player should get the points.

The upper circuit into each score reel is used only during reset. Pulses are generated by the Motor 4A switch and get to the score reels only if 1) the D/Reset relay is active and 2) the score reel isn't showing a zero (the "Runoff" or Runout switches).

You'll have to check your schematic to see exactly how it's done in Swing Along because there are subtle variations on which relays were used but the basic approach will be the same.

/Mark