There are ninety-three (93) screwdriver patents in the DATAMP database. I went through all of them one by one. Most concerned improvements in attaching handles to shanks. Not counting the square shank (meant for turning with a wrench), and not counting permanent tee-handles, I found eight (8) patents that are clearly in the Convertible Lever- or Tee-handle category.
The first of a kind in that group, according to DATAMP, anyway, was 35,337 patented by Julius Thompson on May 20, 1862. It was a lever that folded in and out of the shank closer to the blade than the ferrule. See Pic 1 for the patent diagram.
The second was 428,662, patented by Marcus Bartlett of Providence, R.I., on May 27, 1890. The entire handle pivoted into a Tee position. See Pic 2 for the patent diagram. See Pic 3 for an example owned by Jim Kuch.
The third was 432,928, also patented by Marcus Bartlett (a man obviously driven by the problem...) on July 22, 1890. Instead of permanently attaching the lever, this device was attached to the shank. See Pic 4 for the patent diagram.
The fourth was 821,328, patented by Harry D. Bartlett (of Chicago, and if Marcus wasn't his brother, father or uncle it would have to be a rich coincidence...) on May 22, 1906. Another handle that folds or pivots in and out of a Tee position. See Pic 5 for the patent diagram.
The sixth was 1,000,050, patented by William S. Thompson and assigned to H.D. Smith on August 8, 1911. It uses two solid pivoting halves of a typical "Perfect Handle" and the shank to form an L-handle, a T-handle, or an offset handle. See Pic 6 for the patent diagram and the post above or the H.D. Smith thread for more photos of my example.
The seventh was 1,215,308, patented by John Johnson and assigned to Crescent Tool Company on February 6, 1917. It is the folding or pivoting handle type akin to the first and second Bartletts. See Pic 7 for the patent diagram. Examples regularly sell for north of $200. GJ member OTG has one. I can't remember where he has posted it, but maybe he will add it later.