Fortunately I figured this out since I posted it! I played around with the zones some more and figured out how to get the Maine tax to show.
Here's what I wrote:
I am confused about how to get state tax from the state of Maine (in the US) to show up in the shopping cart.
We have an online store that sells books.
We will not charge taxes unless the shopper resides in Maine.
I published all countries on the Zone screen.
I have one category for taxes: the Default Category. All the books have this chosen as their category.
In System, when I click on "Taxes" the Tax Rule lists Maine as a zone, "Default tax category" as the Tax Category, but Rate is listed as 0%. I had set it as 5% in the Manage Tax Rates screen for Maine. Customer type lists this as a "Company with VAT number". I had checked do not check for a VAT number on the configuration screen.
I don't know what I've missed and would appreciate any help.
Thank you!