I don't know what the policy is on here posting other URL's so apologize preemptively if I am crossing a line but here is the literature on an identical 1950 starting system. It also ties into the transmission operation. Very informative. What a crazy system! https://www.hometownbuick.com/1950-buick-cranking-system-starter/
Brooklyn Beer - I am guessing that you got your starter problem resolved. I am having the same issue on my new 1948 Roadmaster. Only way to stop it is to disconnect the battery and more than half the time when I reconnect the battery I don't have to push the pedal down for it to start. Just turn the key but it stays stuck. I put in a new battery and the cables are all clean and 2 gauge. From reading this post it seems more likely that it is electrical than vacuum but I am going to test the vacuum situation right now. I will say that now that it has a new battery it is doing it less. Before the battery it happened almost every time but now is much less frequent which leads me to believe it is electrical and hopefully just a sticky relay/solenoid (as mentioned above) from the generator. I just got the car two days ago so all is new to me. I haven't found much about this problem online so it must not be common but as time marches on it seems like a real sleeper of a problem that will hit a lot of us. My Buick is original and has been immaculately maintained. The gentleman that owned it for the previous 50 years did everything mechanical himself and did not throw parts at it. He would just analyze and repair. So the car has a lot of 72 year old parts. It would be great to see how you repaired the issue on here for future people. Thank you.