It's an Alumacraft.
There will be a model/serial stamped in the spine of the transom brace that will help your journey with the TWRA. Post it here if you would like me to date it for you. I have copies of the factory production numbers.
It's likely from the '50s considering the lights. Many trailers from that era only offered a single taillight and it was an option. The whole recreational trailering thing was a slow evolution.
For what it's worth, if it was never registered, I'm going to assume it was never taxed at the county clerk. In the absence of that clerk paper, it might be the path of least resistance to have your neighbor "sell" it back to you. The county won't even look at whose name was last belonging to the registration numbers and being a non-titular state, the TWRA will register a bucket if you have paid county taxes on it.
Tennessee is super easy to get a boat on the water - you can literally do a bill of sale on a cocktail napkin - but the counties want their tax money and only then will the TWRA want their registration money.
(the TWRA also offers an actual bill of sale online that will streamline the process)
(also for another hint, take a paper copy of a photo to the clerk when you pay taxes on your $75 boat, if you know what I mean. Make sure the photo shows the current bow numbers. They will reuse them. The brand, size, serial, and year can be entered fresh when you're at the clerk, too. There are spaces for that info on their bill of sale.)
Also for what it's worth, I've been down this registration rabbithole a few times. Sometimes it's much easier to just throw the $20-30 of tax money at it, rather than the esoteric paperwork for the other routes that garner greater scrutiny.
But it's great boat. They're built like battleships. Congrats on owning it again.