In California, on a 2-lane highway, if there were a horse cart being pulled along the road, he would do what any other vehicle on the road does: Use the furthest right lane available for thru traffic (on a 2 lane highway, the only lane for thru traffic). Cars would pass as necessary. If cars were unable to pass, he would pull aside to let them pass (legally after 5 or more, but probably ASAP) as soon as it's safe. Same as a slow car, tractor, or anything except a bicycle, which must ride FRAP per 21202 barring any exceptions (which most cyclists will do regardless of law).
Really, this point of whether you must share the lane on a 2-lane highway under 21654 in CA is moot anyway, because 1) as it stands, 21202 makes 21654 mostly irrelevant for cyclists and 2) I've rarely seen a 2-lane highway with wide enough lanes to share.