My early 90’s Corolla – no FOB, just a plain turn the key system – from a Northern Calif dealership in the OP’s area came as new, unknown to me, with a basic security system installed. Installed by the dealership apparently to protect the car while it was on their lot.
This thing caused me a lot of grief until I finally found it installed in a place where nothing should be.
Good advice above to check with the dealership, I expect they’ll know what’s causing this.