I meant to add this link & hit send without doing so. It is a copy of a 1908 Singer/Bridgeport catalog from the Smithsonian site. As you can see Singer was still making a lot of the various sub-models of the 12(W) at this point in time. You may be able to pin-point yours from the info here.
All Singer machines with a W in the "Model" designation were built in the old W&W factory at Bridgeport CN & most, if not all, were built on W&W design.