Prop 13 does not change if you rent your home rather than live in it. Prop 13 applies to all real property in California.
The only item that is tied to living in your home vs renting is the homeower exemption. for that you have to live in the home. The minute you move out you lose it. You have to file a form when you move back in to get it back.
I have heard that you must have lived in your home, I can't remember, two of the last five years or three of the last five years.
Are you saying that you can rent the house indefinitely withoujt losing the tax base under proposition 13?