rsm dont need chakra mode.
the prime indicator would simply be the TSO or the 9 tomoes on his back and the fact that only his clothes are glowing.
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seems to me that he doesnt use it after his fight with sasuke but then again its only been 2 movies and I highly doubt he ever needs to go full out like that again.
maybe against Toneri but its wierd.
here we see a different version of Naruto's rasengan.
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then we see the same thing with Toneri as well with his Truth Seeking Orbs but glowing.
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but it is not RSM... maybe he just conjures his TSOs but thats at the most.
else wed see Naruto with only his clothes glowing and not completely engulfed with chakra.