I find it curious English not having a singular word for this.
We have a few. It depends on precisely what you wish to describe.
The pure back-and-forth movement, especially whithin limits:
verb [ no obj. ]
move or swing back and forth in a regular rhythm: the grain pan near the front of the combine oscillates back and forth.
• [ with adverbial ] vary or fluctuate between two states, limits, opinions, etc.: he was oscillating between fear and bravery.
Whereas oscillate pertains to the back-and-forth movement of the thing, escapement pertains to the delivery of power (the power of the spring escapes into the cogs that move the hands).
I'd like to find a word that is not as ambiguous
Yes, that is to be avoided.
or context dependent
No. All Indo-European languages (including Swedish) are context-dependent, it is a principle, you can't get away from it. The sense of the word is modulated by the context that it is used in. Refer to the examples in the OED definition:
- the balance wheel oscillates between clockwise and anti-clockwise,
- the claw oscillates between capture and escape,
- the person oscillated between fear and bravery.