How an EM slingshot works
The ball hitting the rubber closes a switch that fires the slingshot coil; the plunger pulls the kicker arm, flicking the ball away. A second switch under the playfield, closed at the coil's end of stroke, usually fires a 1 or 10 point relay for scoring.
Systems
Source: Repairing Electro-Mechanical (EM) Coin Operated Games to 1978, Part Two, Clay Harrell (pinrepair.com)