You should be able to remove the whole thing by simply twisting counter-clockwise then pulling the finial back. The threaded shuttle will just keep twisting until it falls out. It should look something like this:
There are two possibilities. One is that the shuttle (the sliding thing attached to the push rod) is worn. There should be a good 1/64" (0.25 mm) of metal left on the ridges. If that is the case, you may be able to find a donor Eversharp pencil for the part.
The other possibility is that the internal threads are worn. That would be bad. You could try a replacement shuttle with great threads, in the hope that it would engage in what is left of the internal threading. The internals are a brass tube, threaded on the inside, which fits down into the bottom end of the barrel. Not really a do-it-yourself kind of job to replace.
Now that I think of it, if it is internal threading, it could just be a build-up of corrosion on the brass threads. You could also try using a surgical swab dipped in vinegar to react away the corrosion. (Be prepared to use a lot of swabs if that is the case.) This may remove enough build-up to allow the shuttle to engage.
A good little flashlight is good, in any case.
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