No expert on the law here- but I think that the bureau would probably pull your guard card and permit if they were notified by law enforcement that you were carrying outside the scope of your duties.
I found the application for a firearm permit- here. It says:
5. Read carefully before signing below: I understand that my firearm permit will authorize me to carry an exposed loaded firearm of the caliber(s) listed on my permit only while on duty or while directly en route to or from my home, to my worksite or a firearm range (PC 12031 ( d ) (5)). I also understand that no private patrol operator licensee or registered security guard shall use or wear a firearm unless he or she is wearing a uniform. At all other times, the firearm shall be unloaded and kept in a locked container during the course of travel (PC 12026.2 (a) and (b)). If not wearing a uniform, the firearm must be unloaded and locked during the course of travel. Persons authorized to carry a concealed weapon are exempt from these requirements.
What may be important to note here is that there are six restrictions that affect exposed carry statewide in California. Technically, if you adhere to the limitations of those six restrictions, you can lawfully open carry a firearm without alicense or permit issued by any agency. Local ordinances may apply however.