The person you're talking to in the tax office is probably young and inexperienced. A modern VIN is always a long number, but for LOTS of older vehicles it was much shorter. It's even possible that you have the correct VIN and a problem exists between the keyboard and the chair at the tax office... they may need a particular format to search an older/shorter VIN, or they may need leading 0's, etc.
It's also possible that if it's been stationary on a ranch for more than 20 years, its record had been inactive long enough that it was never loaded into the database under the assumption that it had been scrapped or something. I'm sure there's a method for creating a new record if there was never a computerized record and you want to register it.
Here's a link for the TX DMV lost titles page.
There's a form to download and instructions about what you need from the previous owner as well, and it says to mail to (or go in person to) the TX DMV regional office, which for you is probably the one at Fredericksburg and 410. Take photos of the VIN plate and if you find a VIN stamped on the frame. See what they can do. My VIN on the Texas title for my '75 is only 8 digits long.