First off, you have to understand that this forum software is old. Rogean tried updating it a few years ago and everyone threw a fit, so now we're pretty much stuck with outdated forum software. But on the plus side the forums feel like they're from the same era as classic EQ
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In light of the above, I don't think there is any setting you can change to control when posts get marked "read". I could be wrong, but as far as I can tell if you click "New Posts" the forum will give you every new post, and then mark them all as "read" like 20-30 minutes later, and there's nothing you can do about it.
But, to work around it, what you can do is logout, or open a new incognito window, and then come back to the forum. Instead of "New Posts" you'll have a "Today's Posts" link, and that will have all new posts ("read" and "unread").
Or you can just do what I do, and not open up "New Posts" unless you're ready to at least skim through all of them.