I recently purchased a die filer and it is a great little machine. I can see where they would be fantastic for clockmakers, especially when crossing out wheels or making elegant frames.
I have only used it for one project so far, but it was a worthwhile purchase. I got lucky and got mine with forty some files for $50 from a retired tool and die maker. It is similar to the unit shown above but is powered by a gear motor, which slows it down a little more, which I see as being more appropriate. It also has a larger table, square in shape with a very unique table mounting that allows adjustment in two directions so that it can be completely squared with any file that is mounted, or it can be set to any angle that a person might desire. I do not yet have any photos of it but should get some up here.
The files typically have a round shank about a quarter of an inch in diameter. They are also different in that they cut as the file is pulled downward, and not the other way around like a conventional hand file. From what I understand new files can be difficult to find, but they are out there, one just has to look hard to find them.
One word of caution: When you first use one you will quickly learn to keep your fingers away from the edges of your work. If the file happens to lift your part, a finger near the edge manages to quickly slip under it just a bit, getting a nice pinch (and maybe even a nice blood blister) as the file pulls the part back down to the table. Yup, been there, done that!