How do I handle a slight gap on the final deck board?

If the gap is truly only a quarter inch or less, your first option should be scribing the board down tight. You'll want to use a sharp chisel or a fine-toothed saw and work slowly, taking tiny passes. You're basically fitting the end of the decking piece perfectly against the angled face of the joist structure. This minimizes the visible line and makes the transition look deliberate, like it was installed that way. Just be patient; rushing this small trim is what usually creates a noticeable uneven line. But if the gap is slightly more, or if the structural misalignment is bigger than you thougt, then scribing might just look awkward because you're making the deck board thinner than it should be. In that case, you should look at sistering the rim joist itself. You could cut a piece of lumber, maybe a 2x4, and secure it alongside the existing joist structure on that short end, effectively building out the frame. Then, you run your last decking board over this newly extended rim joist. This gives you a clean, full-width piece of decking and eliminates the exposed gap entirely.

If you don't want to alter the frame at all, and you're absolutely sure the gap is negligible, you could use a metal flashing piece or a filler strip, but that's usually a cheap fix that looks like a band-aid and isn't proffesional quality. For a really nice finish, going back and building out that end with another piece of rim joist is the most proper way to solve it, even if it feels like more work. It gets rid of the issue permanently and makes the whole perimeter look consistent.

Ultimately, assess the gap width first. If it's tiny, carefully scribe it. If it's anything more, build out the supporting joist structure and cover it with your last board.

I ran into something like this on my stairs last summer and ended up cutting the board down to fit. It looked fine but it got pretty skinny and the screws barely had anything to bite into. How thin is too thin before a board just isn't worth using anymore? Also curious if a slightly wider gap at the end is acutally a bad thing, since I've noticed my deck boards shrink and swell with the weather anyway.

Another trick if the gap is a bit too big to scribe: rip the last board down to width on a table saw or circular saw so it lands flush. I did that on my build and the final perimeter board ended up around 5 inches wide instead of full size, and honestly nobody has ever noticed. Just make sure you keep it wide enough that two rows of screws still land in solid wood. Also double check that gap is actually the board and not the frame being out of square, because I chased a 'bad cut' for an hour once when the whole rim was racked about half an inch.