I found this post online mentioning the ebike laws for Los Padres National Forest. It looks like you are only allowed to ride ebikes on trails where motorcycles are allowed.
"...the rules for Los Padres National Forest, set by the U.S. Forest Service, limit e-bikes to “OHV trails, or in layman’s terms, where motorcycles are allowed,” says Mayfield. “That includes West Camino Cielo, Buckhorn Road, Camuesa Road, Divide Peak and Upper Oso.” On other LPNF trails, you can’t be on an e-bike, whether you use the electric aspect or not. (Mayfield adds that e-bikes are welcome at Elings Park and many of the Ojai Valley Land Conservancy Trails.)"