Now we are saying the same thing.

Can someone please point out where in the manual it states this is the BU's call?

Disclaimer, I was reading last years manual. But here's what I had. There are no special exceptions for stealing as to who has what runners. Therefore, the BU has the last runner into third. (Which in this case is the runner who stole second). There is a section on stealing that says that the plate umpire should move out from behind the plate and read the play but it doesn't assign the call at third.
Maybe I just missed a section?

The "last runner" is on a batted ball situation.

No one in their right mind would expect the BU to cover a subsequent play at 3rd after a botched play @ 2nd. Shy of being physically disabled on the pitch, there is no excuse for the PU to not be able to cover 3rd.

And yet, some BU will call that play at 3rd from between the pitcher circle and C slot.
What about this with a runner on 2nd tagging up on an outfield fly?

The Umpire Manual for runner on second base only, fly ball to outfield; seems to contradict itself.
For PU - “any play on the lead runner at 3B”
For BU - “the last runner to 3B”

There is no way the BU can get into a good position to make any call at 3rd without the runner being OBS.

What about it? Apples and oranges. To start, the umpire starts in a different position and it is a batted ball. The BU is responsible for the runner tagging up for a possible catch and advance, and the BR should the ball not be caught

No contradiction as the mechanic has to allow for no catch which would create multiple runners. The BU has the lone runner to 3rd on a batted ball.

No manual handy right now, but I think it's page 43 that lists all of the exceptions where the base umpire makes a call at third base. Single runner advancement from second to third on a fly ball tag up is one of the times.

The second paragraph is true in the batted ball case too. That said, I don't really care what the book mechanic is since we all seem to agree on the accepted mechanic. I went looking in the book to determine what it said and that's best I could come up with.

Again, on a batted ball

Sure, but am I correct in saying that there is nothing particular for this situation in the book?

You are correct. That is why I questioned the claim of what the "book" had to say about it.

I have lost which situation you two are on, so please clarify.

Also, is "Single runner advancement from second to third on a fly ball tag up is one of the times" BU covers 3rd; the answer to my question about apparent contradiction?

Runner on 1st, steal of 2nd, runner advances to third. Who has the call per the book?

;) Irish argues that nobody should call it, and I argue that we should start with batted ball mechanics and then discard them by communicating with each other. :D Seriously though, my contention earlier that it is in the book comes from trying to find the closest fit and going with that but I agree it's a long stretch. I'm just not sure that there's anything better.

Without checking a book, I have always learned the PU covers 3rd on a subsequent play (e.g., stealer of 2nd advancing to 3rd is a subsequent play); unless the PU has a play at home.

I think there's somewhat of a shared understanding that this is the right way to do it. But I don't think the book says that.