OK mine didn't have a circlip, that's why I didn't see an obvious wat to open it up. I pried it open gently and it appears this one had already been glued. There was no spring to measure but it should be the same thickness as the inner gear wheel. I measured that at .15mm
The missing gear is called a double corrector, it's for quicksetting day and date, or day and GMT hand on an ICHS. The CHS includes an extra intermediate wheel to reach the shorter radius GMT wheel where ideally the spring would release the GMT wheel from moving while the gear connected hour wheel would flip.
I put one in and am confident this is the same part as the ICHS (top and bottom views).
Since I have no spring to try to fix, all I can really do is try a better glue job. With that attempted solution, there is no need for the other two GMT intermediate wheels either.
After examining this more closely, I think if the two parts of the GMT wheel can be permanently locked together, the GMT and hour hands should be able to be synched. An offset could be done between GMT and local time manually when setting the hands. After that, there also should be no reason why the quickset date function can't be restored since the two GMT wheel intermediate wheels are removed.