[blabbersnitch]

I have fixed a few balance wheel clocks over the years. Most were from old Datsuns and so they operated at 12V. A different circuit to your clock, but for what it's worth, I found either capacitors or transistors (or both) were failing in those clocks, and I would generally replace them all and then they all would work as good as new.

But one clock I fixed was a 1.5V wall clock from the 70's, possibly with an oscillator like yours. One transistor and once capacitor driving the balance wheel. I can't see a capacitor or transistor in your photos. Can you identify either?
If you are not savvy with electronics, the capacitor will be a component with two legs, and the transistor will have three. A 70's era transistor might be in a metallic 'can'.
The capacitor will be easy to replace. It should be pretty easy to find an equivalent (and a precise value match won't be necessary).
The transistor could be tricky. I expect it will be a germanium transistor at that voltage.
I was able to find one for my wife's clock. I traced out the circuit and found a germanium pnp transistor on eBay for a few bucks.
And she's been ticking away since.

Can you get a better photo of the electronic components? Can you identify what is printed on them?