Ensuring user knows scrolling is an option

I have a div that sometimes contains too much text to view at once, and I need the user to be able to scroll.

My concern is that it's not particularly obvious that they need to scroll, especially if the bottom line is fully visible, you can see what I mean here.

The other issue is that while there is a scroll bar, it only appears when the user is in the process of scrolling, and it's very thin and hard to see.

Any ideas on ways to improve the user experience when scrolling here? Should I add some ... to the last word? Should I add a small bar to the bottom with a prompt "Click and drag to scroll?" Or maybe a custom scroll bar? All of the above?