"'No, that he hadn't, my dear,' said Mr. Weller; 'and if you'd
put an exact model of his own legs on the dinin'-table afore him,
he wouldn't ha' known 'em. Well, he always walks to his office
with a wery handsome gold watch-chain hanging out, about a
foot and a quarter, and a gold watch in his fob pocket as was
worth--I'm afraid to say how much, but as much as a watch can
be--a large, heavy, round manufacter, as stout for a watch, as
he was for a man, and with a big face in proportion.


Webster's 1913 Dictionary

Definition: \Fob\, n. [Cf. Prov. G. fuppe pocket.]
A little pocket for a watch.

{Fob chain}, a short watch chain worn a watch carried in the
fob.


\Fob\, v.t. [imp. & p. p. {Fobbed}; p. pr. & vb. n.
{Fobbing}.] [Cf.Fop.]
1. To beat; to maul. [Obs.]

2. To cheat; to trick; to impose on. --Shak.

{To fob off}, to shift off by an artifice; to put aside; to
delude with a trick."A conspiracy of bishops could
prostrate and fob off the right of the people." --Milton.

My dad called the thin, round plate with the "Indian Motorcycles" logo stamped on it (attached with a leather strap) and/or or the whole accessory attached to his pocket watch a "fob", never the watch itself.

Dear musick: I can remember when trousers came with a watch pocket. I had a couple vests, but never wore them.
I never heard "fob" used for anything but the object that acted as an anchor at one end of watch chain, to prevent watch falling.