Lovely watch and your post worked perfectly. It’s very satisfying when the smallest fix gets a watch working again, especially in an auction.
Is this trademark on your watch?
If so, it was registered to Alphonse Boichat & Cie in 1904 according to Mikrolisk.
http://www.mikrolisk.de
Edit: Googling a bit more I found a couple of links that reference Alphonse Boichat patenting the centre seconds movement.
https://www.dieschatzkisteimnetz.de/...e88d477ea5ed04 (In German, I used Chrome to translate).
https://forums.watchuseek.com/f7/191...topics/4924365
I found a listing for the Swiss patent, filed in 1900 and granted in 1902.
https://patents.google.com/?inventor=boichat&oq=boichat