Always the fashion plate, Vader's wears a second cloak underneath his  full cape and armor.  It resembles a sleeveless robe that is left open in the front.  The cloak is slightly shorter in length than the outer cape. It just brushes the tops of his boots, although in some scenes, it appears a little shorter than this.
(* Only in ANH does Vader wear his inner cloak OVER his chest armor. All others, including ROTS, the armor is worn on top of the inner cloak)
I did end up sewing my own inner cloak, with inverted teardrop shaped armholes based on the Darth Vader Cinemacast statue (shown above).   There are patterns for sleeveless robes out there (probably more towards Halloween time) that one can buy.  I like to "wing it", instead.  I picked up a graduation robe from a second hand store for cheap money and cut the sleeves off of it to give me an idea of what I needed to do to the material that I purchased.   I basically hemmed one large rectangle for the back, with two narrower rectangles for the front. I connected  them at the shoulder and up the sides, leaving a large opening on each side for the arm holes.   I used a sleeveless T-shirt  to help refine the tops of the shoulders.  The over-the-shoulder portion needed to be a little narrower in width so that it would sit properly on my shoulders.  It shouldn't be sticking out from under the shoulder bells.
The length of my inner cloak is just below my mid-shin region.  I did this intentionally, to facilitate walking up and down stairs, for I use this costume mostly to dole out Halloween loot from my front porch area.
The
Inner Cloak
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