SauravWest:
That’s a bitch of a wall to put a control or expansion joint in. You have to do the best you can to confine its size/length (along the wall)/shape to a fairly straight line. I would use some sort of closed cell, soft foam, sheet material about .5” (+/-) thick in most of the joint width (wall thickness), to keep mortar out of the joint. I would stop this short of the wall outer surfaces, with enough joint depth for a proper sized backer rod, and then caulk the outside of the joint with a properly proportioned bead of caulking. Talk this over with a good mason, so you and he know what you want and what you are getting. Lots of them will butcher this if you let them. Talk with a good masonry supply house for ideas and specific material names.

I've inspected a lot of stone walls; random rubble masonry doesn't have any expansion joints. With that said, people have different descriptions of RRM. IN NYC RRM is just that, stones piled/laid up; no (or minimal at best) horizontal or vertical continuity of joints between adjacent stones; some surfaces may be cut to get things to fit. Where you are, is ashlar considered RRM? Again, where I am, ashlar has cut bedding surfaces. Ashlar can have any expansion joint. Use caulk that complies with Federal Specification TT-S-230 Sealing Compound, Synthetic-Rubber Base, Single Component, Chemically Curing. The caulk would be applied over premoulded joint filler meeting the requirements of ASTM D1751.