It just started happening about a month ago. Right before I put the car on blocks to work on it so the battery has been disconnected for a few weeks. I think I sat in the car and locked from the inside and still heard the noise.
As per the plastic gear. It reminds me of my old Saturn. The odometer had a plastic gear wheel that wore down. A guy used to rebuild them with a similar part from a hobby store. Might be worth looking into.....