Hi Beck
here is not the best place to ask Your questions, this: https://pinside.com/pinball/forum/forum/tech-em is the place.
You have started here in "restoration questions" -so lets handle THIS topic in here.
I want to be sure we are talking about the same goodies -> http://www.ipdb.org/showpic.pl?id=2253&picno=8473 near the flipperfingers are the so called "Shooter Coils" (activated by "Shooter Relay"). Quite a bit upwards are the "Eject Coils" (activated by "Eject Relay"). Great, ipdb has schema and manual.
AAA: Do the Shooter Coils "fire / kick" - then let go - after a short period of time again "fire / kick" - then let go --- and on and on ... ?
BBB: Do the Shooter coils "pull-in" and pull and pull and pull - at no time let go ?
I assume You have AAA - therefore I believe within this period of time the Score-Motor turns and turns and turns - am I right ? I look-up -> http://www.ipdb.org/machine.cgi?id=2253 -> manual-page-15 (ori-13) -> I see "Shooter-RELAY" listed as "M 29-1100 mounted on underneathside of playfield". Please turn-on the pin and look at this relay -> CCC: Does is "fire and let go" - again and again and again - as the Score-Motor is turning and turning and turning ? OR - DDD: The Relay pulls-in and never let go ? OR - EEE: The relay never pulls-in.
If You have "AAA and CCC" read-on - IF NOT: Do not read-on.
"AAA and CCC" is (95% chance) caused by a faulty-always closed Switch there (underneath where the ball rests) - it can be either side. Check the contact-points -> are they wide apart / open ? Also check the solder-lugs where the connecting wires are soldered-on -> maybe a drop of solder has fallen there - maybe one blade (and so the the solder-lug) is bent and makes contact (?).
Some theory: Williams lets You start a new game ONLY when the game before has ended "normal" - means all ball have been played - last ball rolls into the Outhole (between the flippers) and the Game-Over-(Interlock)-Relay has tripped and the Game-Over-Light in the Backbox is illuminated.
If the player has ended the game before "abnormal" - lets say the 2nd ball has landed in the "Shooter place" -> player bangs a SEVERE TILT -> the game is ended - BUT the ball is (in the shooter place) - the ball is NOT in the Outhole. So before starting a new game: Williams WANTS to have the ball in the Outhole - in some way the brain of the pin gets the information: ball is in Shooter place -> so the brain of the pin orders: Out, out, out --- then we can start a new game ...
Please write about AAA, BBB, CCC, DDD, EEE - and write about "Switches underneath the Shooter place". Greetings Rolf