There are no screws visible and the bellows are glued in. Does the front trim need to be taken off? Or do you think the screws are accessible done the back?Also, how do you get the wire to pull the second bellows down, it seems to be stopping as the wires rub.
The second bellow is activated by the first when it falls. It should kick the bent wire off from the lever that holds it. Those novelty cuckoo's are hard to get set up right. They cuckoo once every 15 minutes. Just one single call each time. Do a search for "propeller clock" for more info.
The clock isn't really built to be serviced. In order to split the movement plates one needs to straighten the tabs that are the extensions of the plate pillars. After reassembly, one needs to bend them again to hold the movement together. When you do it a couple of times, they will break off.
I have made a movement like this serviceable by straightening the tabs, then drilling small holes into them just above the plate so than tapered pins could be inserted.