I feel that you actually do have a mechanical pencil here. [emoji106]
Here's a pic of the original patent from 1822.
Nice finds,
Dave
"A mechanical pencil, also clutch pencil, is a pencil with a replaceable and mechanically extendable solid pigment core called a "lead". The lead, often made of graphite, is not bonded to the outer casing, and can be mechanically extended as its point is worn away as it is being used. Other names include microtip pencil, automatic pencil, drafting pencil, technical pencil, click pencil, pump pen, pump pencil, lead-holder, pacer, propelling pencil, pen pencil, and lead pencil. Mechanical pencils are used to provide lines of constant width without sharpening in technical drawing and in quick, neat writing. They have also been used for fine-art drawing. Since they do not have to be sharpened, they are also very popular with students. Mechanical pencils were first used in the 18th century, with many designs patented in the 19th and 20th centuries.
Conrad Gesner described a lead holder pencil in 1565, but the lead had to be manually adjusted to sharpen it. The earliest extant example of a mechanical pencil was found aboard the wreckage of HMS Pandora, which sank in 1791. The first patent for a refillable pencil with lead-propelling mechanism was issued to Sampson Mordan and John Isaac Hawkins in Britain in 1822. After buying out Hawkins' patent rights, Mordan entered into a business partnership with Gabriel Riddle from 1823 to 1837. The earliest Mordan pencils are thus hallmarked SMGR. After 1837, Mordan ended his partnership with Riddle and continued to manufacture pencils as "S. Mordan & Co". His company continued to manufacture pencils and a wide range of silver objects until World War II, when the factory was bombed. Between 1822 and 1874, more than 160 patents were registered pertaining to a variety of improvements to mechanical pencils. The first spring-loaded mechanical pencil was patented in 1877 and a twist-feed mechanism was developed in 1895."