Thank you for the helpful responses!
While testing your code samples, and more of my own, I began to question the requirement that the cursor be inside a table. For example, what if the cursor is immediately AFTER a table? That should be OK.
Through trial-and-error, I learned that this instruction...
Code:
Selection.Tables(1).Select
...selects the table above when the cursor is on the blank line that follows a table.
My guess is that the blank line inherits the formatting carried by the end-of-table marker. It's as if the blank line is programmatically part of the table that precedes it. But the blank line doesn't get selected.
I learned a lot today!