It is essentially an "AVRI late 70's Precision with an added hot Jazz pickup and a 3-way switch".
The body finish is nitro lacquer. The neck is glossy front and back. It has a B-neck profile (1.625 at the nut) which is very comfortable. The tuners are '70's style, probably the same as a AVRI '75 Jazz. The headstock decal is the later '70's style without the huge "PRECISION BASS" font. But the 3-way switch is what makes this bass for me. I had a '00 Hot Rod Precision which was similar in concept but the TF is the better instrument...as it should be, given Fender's asking price as compared to the HRP...which was based on the American Standard of the time.
However, the TF lists for just $100 more than an AVRI '57/62 Precision which seems like a pretty good deal for what you get. But as you said, hardly any Fender dealers have this model in stock and I've seen very few fretted ones come up on the used market. I've yet to see another one in person. Maybe this explains why Fender hesitates to add more P/J's to their already overloaded product line.
Here's a full body pic: