The short answer is that your game is behaving correctly.

A better answer is that the Player Unit won't advance out of the Player 1/Ball 1 position until the ZB/1st Ball relay in the Control Bank has tripped and closes a switch. After that the Player Unit will advance every time the ball rolls over the Trough switch between the out hole and the shooter lane.
Big Shot Add Player (resized).jpg
The ZB/1st Ball relay only trips when 10 or 100 points are scored (via switches on the N and M relays) and it remains tripped until the game starts over. I'm not familiar with Big Shot but how often do you hit a 1000 point target and then drain without hitting a 10 or 100 point target?

/Mark

"Jungle Queen/Princess" (1977) and "Fast/Quick Draw" have the same thing - 1000 pt doesn't activate the first ball relay, only 10 and 100 pts. But it makes sense on both those machines since you can't hit anything worth 1000 (or 5000) on that machine without hitting something else first or second.

But with "Big Shot", as the OP says, you can make those 2 lanes beside the center lane that give you 1000 pts and then, down the middle. I used to have access to a "Big Shot" - would have been fun to try to see how many times I could do that in a row, getting that first ball over again and again, until I hit something else.

Jungle Queen U relay (resized).JPG

Just checking around - "Big Brave" (1974) has it as well. I've never played that game, but it looks like it might be possible to get the ball onto the flippers without hitting anything, then crank the vari-target for several thousand pts, then let it drain. Probably be a one-in-a-million shot, though....at least, for me.

I hope all the cheaters out there are making notes on this...

Looks like a bunch of the '70s Gottlieb machines do it this way. "Royal Flush/Card Whiz" is an exception, probably because on the 3-ball setting, the pop bumper up top is worth 1K - you could get bunches of points and then drain without losing your first ball.

No, it's simply that they want to offer the potential of adding more players until ZB kicks in. This behavior is only seen on multi-player games. There are some edge cases that they didn't feel were worth covering.

Scoring only 1000s was one of the edge cases. They left out that switch to reduce the BOM cost.
.................David Marston

That makes perfect sense! I always thought it was a ball-save feature, but it didn't seem fair that the 1st player gets it and others don't.