I see what you mean. The "existence" part I suspect is a trick. I think "That thing going on for the ride", is actually just a feeling evolved for a bodily purpose.

The body is doing the ride, with all its chemical gradients pulling the levers, and the thing we call Consciousness it's just "the feeling of the ride" which has evolved to keep some temporal/spatial unity. You could have legs, and memories, without being able to connect them to you.

For example, without that feeling of unity, the brain wouldn't not know which subject all the things are related to.

Something would be thirsty or hungry, but it wouldn't know that is the same thing with those legs and memories that it was referring to a just a moment ago.