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Unfortunately, based on what you posted here, I doubt that you have access rights across this parcel.
A "prescriptive easement" rarely exists (it is a form of "adverse possession" which also rarely exists, particularly in states such as California which, in addition to occupying the land also require you to pay the property tax in order to establish a claim to ownership).
Similarly the notion that your property is landlocked is not quite true. Your property is not landlocked in the sense that you cannot access it, you simply do not have access to the public recreation areas in the same manner that you would if the neighbor would allow access across their private property. (This is not landlocked property).
What you have been enjoying is commonly referred to as a "borrowed access" (similar to a "borrowed view" - when a property enjoys an unobstructed view due to an undeveloped neighboring lot, then objects when a neighbor suddenly builds on the lot obstructing "their" view).
However, like most things, this does not mean that there cannot be some reasonable argument for an extension of law or some claim that can be made to force your neighbor to open their private property to your personal use.
(See: http://blog.aklandlaw.com/2010/10/articles/easements-1/exclusive-prescriptive-easements-no-equitable-easements-maybe/ for a discussion).
If you wish to pursue such a legal claim I would suggest that you speak to a local property law attorney with some litigation experience, and prepare to spend a fair amount of money in litigation expenses (your neighbor is not reasonably going to be expected to "roll over" on this one and grant access across the property they just paid for - so be prepared for a legal battle to get this access).