I figured it out. The point is to unscrew the crown and keep it in 0 position when pushing on the farthest/southern spot on the lever from the stem (close to the letter "p" in "push". Notice that the image above is when crown in position 2.
Depending where you are based it may be better to buy from a wholesaler such as Cousin here in the U.K, you say the clock is fitted with a pendulum so you will need a movement with a drive unit built in for the pendulum. As far as repair goes clock repairers would not waste time trying to they would just do a straight swap out of the movement, you need to identify the movement fitted cousins have Hermle and Seiko versions available:
Also bare in mind that you would need one with the correct shaft size.