Total shot in the dark - can you identify this part?

[Frogmella]

I am currently running a 997.1 C2S which recently developed some AC issues. Specifically, the blower changing speed on it's on accord. Around 6 months ago my local Porsche specialist replaced the controller unit on the dash.

Last week my AC and fan blower died completely. Porsche Specialist diagnosed a faulty blower motor relay (the little red hedgehog looking this that lives in the passenger foot well somewhere) This part was replaced today and after arriving at home my blower starts going haywire and switching speed along with some almost mechanical grinding/whirring noises from the dash. My blower then stops dead AGAIN!!! For added fun, I live in Florida and now summer is arriving it is getting rather hot....

As I cursed the gods and got out of my car I noticed a little cog/wheel on my passenger seat that looks like it has snapped. Is anyone able to identify what this is and where it may have come from in the course of changing out a blower motor regulator that lives under the glovebox? Given the strange mechanical noises coming from the dash I am concerned this is linked...

Given the repeated visits to the garage and the lack of progress being made I think the issue may become contentious to resolve so any help to guide me in the right direction and to fight my corner are most welcome.

[Frogmella]

I did think of going through the part diagram but if the cog is a component of a larger part it may become a little tricky.

Hondafanatic - it is actually a large black cog in an even larger hand