Using the category builder in the icons above the Biography text area, entering Spanish American, Tennessee shows 1st Regiment, Tennessee, Spanish American War, which is shown on his gravestone. If you select that category entry, you could copy the category and enter it after unit= in the template, also, because that will convert to the category. Then, you can remove what was retrieved using the category builder. I do that to get the correct wording.
The information about him serving should also be in the biography, not just in the sticker, since it is part of his story. It doesn't look like you have the headstone image in the sources, although you have attached an image.