There's a Stephen B. Gardiner (b. abt 1817 Rhode Island) in El Dorado, CA from the early 1850s thru the early 1870s--presumably for the gold rush.
About 1855, a Stephen B. Gardiner apparently marries Betsy A. (b. abt 1831 England) he has three children: Mary E., Joseph, and John from abt 1856-1862 in CA.
This Betsy then marries widower David Edson Norton by the 1880 Census.I don't know if Stephen is out of the picture because he died or if he returned to Rhode Island.
Here's what I see in the Censuses for them:
1860: El Dorado, El Dorado, CA G.B. Gardener 43, b. abt 1817 Rhode Island [In 1870, he's Stephen B. Gardiner, so the G. is likely an S.] Betsey 30, b. abt 1830 England Mary 4, b. abt 1856 CA Joseph, 2, b. abt 1858 CA Burnice Payey 12, b. abt 1848 Michigan
1870 US Census: Mud Springs, El Dorado, CA (July 7, 1870) Stephen B. Gardiner, 53, b. abt 1817 Rhode Island Betsy A. Gardiner 41, b. England Mary E. Gardiner 14, b. abt 1856 CA Joseph Gardiner, 12, b. abt 1858 CA John Gardiner, 10, b. abt1860 CA Source Citation: Year: 1870; Census Place: Mud Springs, El Dorado, California; Roll: M593_72; Page: 79; Image: 158.
1880 US Census in District 54, Mud Springs Township, El Dorado, CA
Name Age David E. Norton 50, farmer b. NY to parents b. NY Betsy A. Norton 49, b. England to parents b. England Dora L. Norton 22 (daughter) b. CA to father b. NY, mother b. ENG Earl E. Norton 16, b. CA to father b. NY mother b. Ireland Joseph Gardner 21 stepson, b. CA to father b. MA and mother b. ENG John Gardner 19 stepson, b. CA to father b. MA and mother b. ENG
Hope this helps; perhaps this is your Stephen B. Gardiner rumored to be in California in 1853.Virlene