I seem to remember that there was a way to figure out where a book is in the FIFO system.  Not a newly posted book, but one already on the bookshelf.  Of course, I can't remember the method now, and maybe I'm hallucinating the whole thing.  Anyone know this trick?  Thanks.

You can only find out how many books are posted, you cannot tell where a particular book is in the FIFO line.  To find out how many copies are posted, add the book to your reminder list.

What Mary said

but maybe hallucinating will give helpful information...

People have been asking to have that info available for years.  I don't know how really helpful it would be. I've posted books with hundreds of copies and had them requested from FIFO within a just a few weeks.  On the other hand, I've posted books that only had a few copies or even just mine posted that sat on my shelf for years. 

Still, lately I've only been posted books that have just a couple of copies or are WL and donating everything else. But that's because I have a good stash of credits and no space. I will still sometimes post a book I plan on reading soon before I read it so it works its way up FIFO in the meantime. But not if it's only got a few copies posted, is a doorstopper or with more than 1 or two at a time.