There is no information in the current B738M AOM that tells crews that the "MCAS cycles between the left AoA and the right AoA sensor". What is the source for the above statement?
I'm not the person you replied to but I tried to find some sources for it, I could only find an article titled "737 FCC Pitch Axis Augmentation - Command Integrity Mandate for Dual Channel, Fail-Safe" on satcom guru.
They assume that's the case because that's how the similar speed trim and mach trim functions work, the functions are controlled by the active FCC, and the active FCC changes when the plane lands, and reverts to one the left side after a power cycle.