OK. Got me thinking and I tried it, but it did not work. (May have done it wrong.) I did the following instead and placed this - as an example - within the short code for the tab that contained the longer text.
<div style="overflow: auto; height: 200px;">
Some example text
The above did work and I did not put anything into the CSS sheet.
Curious now if I could make this more standard for all of the tabs? In other words, for any tabs created, always make them 200px height, and the scroll bar would show up if needed?
Note - My solution is pretty clunky but it works. The problems happen when you switch back and forth between Visual and HTML mode in the WordPress editor.
Still looking for a better solution if anyone has ideas...