Single ball williams machines of that era don't check the status of the outhole switch when starting a game. It assumes the ball is there and launches it without taking into account its status. Nor does the switch in any way connect directly to the solenoid. That's completely under the cpu and software control.... software senses switch close and reacts to it, by counting down the bonus, advancing to the next player/ball/game over. Next player/ball causes the solenoid to activate under software control. No switch sense=ball never ends (like you're seeing)

Sounds like you have a dead switch. Time to try running the switch test! Put all the drops up and the ball into the drain see if it shows up. If it doesn't, press on it manually or use something to hold the blades closed. Still not showing up, look for broken wires. Outhole switch is likely the very last switch on the chain.... tug gently on the wires where they are soldered to the blades.

Go read pinwiki in the system 4-7 section, switch matrix is covered really well there, including how to test.
http://www.pinwiki.com/wiki/index.php?title=Williams_System_3_-_7#Switch_Problems

https://www.marcospecialties.com/pinball-parts/06-8AR-10

random example

switch blade is what the contacts attach to, there are at least 2 in your switch... they're built up into a little stack with bakelite spacers in the middle with 2x plastic tubes to hold them together. Sometimes there's a dead blade as well that helps limit the travel of one of the blades.

dead blade just refers to one that's there to make sure one of the blades with a contact on it doesn't go too far - it doesn't mean it's a "dead" blade in that it's not working.

You can inspect the contacts and clean them with a piece of file folder or a business card or really any piece of paper - put the paper between the contacts press down on the other contact and run the paper back and forth on it. You will see some black stuff on the paper. If you then look at the contacts they should have a gold finish on them - if it looks broken or silver, the plating is gone and is most likely the source of your issue.

You can test the connection back to the mpu by putting a test clip lead on the 2 solder parts of the blade (or the blade itself) and go into switch test. Put the lead on with the machine off so you don't accidentally short solenoid voltage to the switch matrix.... very bad things happen in that case. Then turn the machine on and go into switch test see if it's showing closed, if it doesn't you probably have a broken wire back to the mpu board.