How do I scroll through messages at my private terminal?

When browsing my messages, there's a big arrow near the bottom that I can only assume is letting me know that there are more messages off the bottom of the list. When I press down arrow, however, it only makes the "invalid action" sound.

Is there something I'm missing, or is that arrow not indicating there are more messages?

I'm fairly sure in this case that it means you do not have any more messages to read, despite the arrow blinking. When you have more messages than will fit on your screen, then you get a red scroll bar on the right hand side which you can click and drag to move. I've highlighted it in the screenshot below.

This shows my messages scrolled to the very bottom of what I have received. When I hit the bottom, the arrow at the top appears letting me know there's more up above. Given the lack of scrollbar in your case, you likely just don't have any more and it's blinking because that's all there is on the screen.

I'd like to note that oddly enough, despite the mouse scrollwheel working elsewhere in the UI (like the Journal and Codex), it does not in this case, and requires you to click and drag.

Usually that arrow means you have more messages, but I think in this case it's incorrect - the email you have highlighted is the first one in my list, except for one that is regarding my KoA promotional items.

I have more mail than what fits on one page, and when I scroll down past the first page's worth, the arrow moves to the top.