Uiua, 18 17 bytes
/◇⊂⍜▽¯◿2⊛.⊜□≠@A⌵◇⊂⍜▽¯◿2°⊏⊜□≠@A⌵.
/◇⊂⍜▽¯◿2⊛.⊜□≠@A⌵◇⊂⍜▽¯◿2°⊏⊜□≠@A⌵.
⌵. # Push an uppercase copy
≠@A # Mask of those not equal to A
⊜□ # Partition, boxing each string
⊛.°⊏ # Copy, push the range 0 to its length
◿2 # Modulo 2 (alternating 0s and 1s)
⍜▽¯ # At positions with 1s, swapcase
/◇⊂ # Reduce by joining each unboxed string
💎
Created with the help of Luminespire.
I don't like formatting Uiua explanations like this since it's hard to explain everything on one line (especially because I like to do pretty in-depth explanations). Particularly for Uiua it can feel awkward reading the code down and to the left while reading the explanation all the way to the right. But, there's a clear tradeoff, doing explanations this way takes much less time, and I don't have that much time right now so this'll do.