"P32T" is the ICAO designator for the T-tail Lance II, PA-32RT-300 and turbocharged PA-32RT-300T, both with Hershey-bar wings (1978-79). All of the production T-tail Lances had Hershey-bar wings.
But as Paul Harvey would say, "here is the rest of the story ... "
The 1980 model retractable was supposed to have been the PA-32RT-301 and -301T, dubbed "Lance III". It was like the Lance II, but with Saratoga-style tapered wings and a longer stabilator on the T-tail. A 1978 Turbo Lance II, N20816 (coincidentally the one on the production line just before Rusty's N20817) was pulled off the line and modified to become the Turbo Lance III prototype. Suddenly, though, Piper decided to go back to the low tail, and N20816 had a quick T-tail-ectomy and became the first PA-32R-301T Turbo Saratoga SP.
Just today on Facebook a former Piper marketing executive posted that he flew N20816 back in the day. When Engineering sent him the data sheets he ran the W&B and found he could not load more than five people in it and stay within the CG envelope. He called corporate and the Lance III project was canceled. That was on a Thursday, he said, and by Monday N20816 was ready to fly with a low tail. According to Roger Peperell's exhaustive book on the history of Piper designs, some 35 Lance IIIs either completed or under construction had to be modified to low-tail (Saratoga) configuration to start the 1980 model year.