I don't think the N64 used cube maps for this type of texture. Instead they overlayed a black and white cloud or streak texture (like this texture used on the master sword in OoT), and overlayed it on top of the base texture.
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Then, instead of mapping that texture with normal UVs, they use the
surface’s orientation relative to the camera (its
normal direction) as if they were UVs. This way, when you rotate the object or the camera, the texture appears to slide.
Here;s a screenshot of the shader I found someone using in Unreal engine for the same effect, this time for the Mirror Shield:
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I was able to recreate this set up in Blender like so, and it gave me the desired results like in the OP's first example with the Perfect Dark logo etc:
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