I'm trying to create a tag for a song; in the Song Settings I have Tag Exists checked, I have set the tag to start after bar 32, and then play from bar 33 to 36, and clicked 'OK';
Generate 2 bar ending is unchecked.

However, when I reach the end of the song all that happens is that the normal 2 bar ending is playing when I get to bar 33 - the song appears to carry on to bar 36, but nothing is playing.

How to I get it to play what's written?

[BiaB 2020, MacOS 10.14.6, MacBook Pro 15" Mid 2012]

First, I'm assuming you have more than one chorus, tags don't work otherwise.
From your description, it sounds like you have frozen tracks... unfreeze and regenerate?

In answer to my own question, it appears that changes in song structure are not getting played back as written until I have saved the file, quit Biab and restarted.

This is happening every time I change anything like a repeat or coda; the change is displayed, but does not come out in playback - ?!
Nothing is frozen, btw.

Disable Fakesheet mode in the chord sheet (button on the Views panel), so that the repeats are expanded and you are seeing all bars in the chord sheet. There are a couple of ways to add repeats - it can either generate or not generate the new bars for you. Viewing all the bars may clarify what's going on. Can you provide a simple specific step-by-step example so that we can try the same here?