Thank you for the new, better photo, and for the measurement correction.
I did a bunch or additional research, and now believe I have reached 100%-certainty about the ID of the object you dug. Due to the research-results, I must retract my initial opinion that it is a horsegear rosette. As mentioned in my latest post, the melted fillermetal damage "obscured" the object's attachment-form.
I found a photo which I believe shows what your object's attachment-form was, before the fire-damage happened. The photo shows 3 excavated actual horsegear rosettes, and what appears to be your object. Its back had a wide thin rectangular "tunnel" through the fillermetal, to accept the thin bar-shaped shaft of the clock's pendulum.
I previously mentioned that the rim of your object's brass face is "curled-over" on the back, similar to a 2-piece button's front-section. (The "curled-over" rim is clearly visible in your new photo of your object's back.) Note that the backs of the brass-faced rosettes in the photo below do not have a "rolled-over" edge ...but the clock-pendulum weight does.
So, I think we can green-check your mystery-object now. It is indeed a clock-pendulum weight. Anybody disagree?