The activation data storage locations is an implementation detail. The location (a) doesn't matter and (b) has changed in the past, will change in the future (c) depends on a number of factors.
Short answer: just use the TurboActivate API. Messing around with files gets you absolutely nothing.
Want to deactivate? Use TA_Deactivate().
Want to activate? Use TA_Activate().
See: https://wyday.com/limelm/help/getting-started/
https://wyday.com/limelm/help/activations/
The activation data is not portable. Meaning it's locked to that particular computer (which makes sense, because TurboActivate is node-locked licensing). If you're looking for something to "save" or backup, then what you're looking for is the product key itself. Not the activation data.