Yes, there WAS a Red squadron of Y-Wings at the Battle of Yavin, but only in the novel. In the novelization the Y-Wings were Red Squad, and the X-Wings were Blue Squad. This was changed after it was realized that the blue markings would have become transparent during blue screen work. That's also the reason why when you see R2 in the X-Wing cockpit in every movie, he's got black panels instead of blue. This was corrected in the Special Editions. I have recently made my version closer to the pictured version, making the cockpit yellow and the wing markings red.
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