We can absolutely nix the historical service ID you have.

She was, in fact, built new in 1879 as one of two identical Baldwin steam
dummies for the Market Street Extension Railroad (then a Southern Pacific
Co. affiliate company) as either No. 1 or No. 2; we believe she was No. 2
(see CSL photo, attached).  This positive ID comes from BLW serial
numbers "4-11-1/4C . . ." stamped in numerous frame and chassis parts
found under many black paint layers, a flawless BLW birth certification,
that linking us to preserved BLW Order Books data sheets showing the
actual order form and relevant construction details, those preserved at
DeGolyer Library, Southern Methodist University, Dallas TX.  These two
weighed 11 tons when new, complete.

Her history in SF was short; SPCo was preparing to extend its cable line
into the Hayes Valley (Castro Street) from Valencia Street in 1878, and
used the dummy line for about 9 years until the substantial cable
infrastructure could be installed, the dummies serving that suburban
traffic link.  In 1889 both steam dummies were sold off, No. 1
apparently going to a Humboldt County lumbering outfit, and No. 2 to the
Navarro Mill Co. mill at Navarro, CA.  That outfit was heavily mortgaged
in 1891 when the Panic hit, and the numerous notes- and
mortgages-holders called in their loans.  A lengthy series of legal
fights began, but ultimately the Sheriff of Mendocino County acted for
the creditors and auctioned off the entire Navarro property.  However,
the sawmill and some railroad equipment standing cold next to it, had
burned in 1896, one of the victims being the dummy loco.  That blaze
consumed the wooden dummy body which had been overpainted black.

Enter Union Lumber Co. of Fort Bragg, who bought the scorched dummy for
unclear reasons, but took it by steam schooner to Fort Bragg and rebuild
the engine portion in the Fort Bragg machine shop shared with ULCo's
logging railroad (the future California Western RR & Nav. Co.).  ULCo
was noted in the local weekly paper as having tested the rebuilt engine
as a switcher, perhaps thinking of assigning it to the little Fort Bragg
- Glen Blair daily shuttle trains that brought Pudding Creek Lumber Co.
milled redwood to the ULCO shipping wharf at Fort Bragg, and generally
ferried people and small amounts of freight into the Glen running
eastbound.  However, in 1903 ULCo became one-third owner in a
reorganized form of the Pudding Creek Lumber operation, whereby that
became the new Glen Blair Redwood Co.  Sometime between 1899 and 1902,
the Pudding Creek operation decided to build its own short logging
railroad into the timber along upper Pudding Creek (east of the Glen)
and used the ex-dummy as its first construction engine.  It thereafter
became GBRCo's M of W motive power, and stayed at Glen Blair intact
until the company quit railroad operations in the late 1920s.  The Dinky
was then stored there outdoors until 1941 when scrapper arrived to tear
out any scrap-worthy iron and steel while ULCo sold off the idle Glen
Blair mill machinery to others.

Dinky was to go to the scrappers, but the local Glen residents "stole"
it and hid it on private property, first under tarps, and then under
carefully cut blackberry brambles looking as if it was just another
mound of Himalayan blackberry vines.  Apocryphal?  Nope.  Eventually,
ULCo execs figured out the sleight of hand act, which no longer seemed
important as the scrappers had cleared out five years earlier.  In 1947
the Glen folk convinced ULCo president Otis R. Johnson to "accept" Dinky
as a heritage artifact, and since Otis was a history lover, he did so. 
It was then lifted onto a truck and moved to Fort Bragg.  The rest is
better known history.  It technically remained the whole time in ULCo
ownership, and was gifted to the City of Fort Bragg when ULCo successor
Georgia-Pacific Corp. donated the ex-ULCo Guest House (turned into a
museum by G-P in 1973) with its entire ex-ULCo heritage museum
collections.