Monitoring a 200 year old dry laid stone wall for movement
That's a lot of potentially moving parts. I know very little about scanning, but that would seem to be the way to go. Otherwise, you might set a hundred check points per a certain length of the wall. That's a huge amount of data to compare manually and one heck of a lot of shots from a very solid set up using the same equipment every time.
Just based on your first photo, I would say YES, it is moving.
I know this doesn't help with your question. It really depends on what equipment you have available.
I don't think you will find the rate that it is moving at to be constant but rather a function of the degree of water saturation of the retained soils as the weight bears down on the wall. In other words when dry there's very little to no movement but following a prolonged rain event the movement accelerates with the increased load and soil lubrication.
The scope needs more definition.
The best approach is to measure it with the equipment and procedures you are comfortable with and report accordingly. Keep it simple and repeatable and do not report anything beyond what you can measure.
Doubt there is enough work there to learn too many new tricks.
If you don't have access to a scanner; I would place targets, at strategic locations and measure those at standard intervals from solid control. Report your findings in a spread sheet, created in excel. What they do with the data, is up to them.