Frédéric Ecaubert ran a factory that appears to have specialized in producing watch cases and lockets - and had been granted a patent for a machine associated with this work - No. 531789 - on January 1st 1895. Heavily involved in the watch trade, another of his enterprises involved devising another form of spindle work holding for watchmakers' lathes. Sadly, this invention proved to be a dead end and was not taken up, as far as can be discovered, by other makers. Even so, unlike so many watch-lathe-related patents, his lathe was manufactured and at least one example, complete with 38 of its special collets (or chucks), survives to this day. It's shown below, towards the bottom of the page, with its bed carrying cast-in lettering proclaiming "F. Ecaubert NY Pat Jan 10, 1882". For a lathe intended for use by a watchmaker, it appears to have been of less than impressive quality and more resembles one intended for casual amateur use.
An interesting feature of the patent was a large disc, "B" in the drawing, threaded on its inner bore and formed with a gear-like gripping surface that surrounded the spindle and, by turning it, caused the collets to be opened and closed (the drawing makes the system clear). Another part of the patent was a most helpful idea; a bar ("H" in the drawing) was hinged to the back of the bed and was fitted with a stud on its end that engaged holes in the periphery of the spindle "backplate" to lock it while chucks were changed.
The problem that Mr Ecaubert faced was the fact that by the 1880s, Charles Moseley's 1857/58 design* of a hollow-spindle lathe for watchmakers with its draw-in collet and the incorporation, by 1862, of high-speed, hardened steel spindles and bearings had become the accepted standard - and one almost impossible to improve upon. The Moseley lathe was first produced in 1859 and resembled what is now known as the "Geneva" type with its round bed and generally light build. Today - with the addition of anti-friction bearings in some cases - the same design prevails with the two most common types, the light "Geneva" and later heavier WW (Webster Whitcombe), using it exclusively.
*..from a patent taken out by George W. Daniels and a Mr A.Fuller who, both with Moseley, were residents in the watchmaking and precision engineering centre of Waltham. For details of this important development, see http://www.lathes.co.uk/moselely and https://www.lathes.co.uk/daniels-moseley