I don't quite know why this thought seems novel to me today, but: Emotions are the thoughts of another brain.
This is sort of inherent in the triune brain model, which like all models is partly wrong but I think true enough to be functionally useful here. The vocabulary for the parts (neocortex and limbic system) and our understanding of consciousness is all we need here.
Our awareness, our sense of consciousness, is definitely neocortex - we can think about our working memory, do logic there, and be aware of what we're thinking about there. The limbic system (septum, amygdalae, hypothalamus, hippocampal complex, and cingulate cortex) is physically distinct, isn't fully connected to the six-layer network structure of the neocortex, and exists in a lot more animals than a neocortex does so there's definitely some sort of evolutionary story there.
So the limbic brain is like this "other" brain, also in "our" heads - because we definitely conceive of our higher order thinking as being our real self. The cognitive activity and signals coming from the limbic brain, however, get labeled "feelings". Feelings are verbalized as a duality against (rational) "thought": We think things, and we have feelings - we don't "have thinkings" or "think feelings" in our language. But they're made of the same stuff!
Feelings are just thoughts that we're not conscious of in the same way as our neocortical thinkings. Rewind evolution back past apes down to, I dunno, about dog complexity. There's enough emotional resonance there between us that most people would say "yeah no question, dogs have feelings". Now, dogs' brains do a lot of the same things that ours do, and yet they're not too bright about many things that take more complex thinking. They are thinking. Thinking is just "brains doing stuff". Thinking doesn't mean "human consciousness" - even jellyfish "think", more or less, almost without brains.
I don't know why I had them separated so much in my own understanding. Feelings "feel" different not because they aren't thoughts, but because they are thoughts that are wired up to our conscious brainparts in a weird way that we don't fully comprehend or understand! I promise I am not stoned or anything... this just fits into the landscape of Internal Family Systems, trauma-aware emotional reprocessing, Bio-Emotive Framework, etc etc etc and my own integration is finally catching up and going beyond these useful-but-wrong words of "feeling" vs "thought".
I have usefully worked with the "little five-year-old me inside of me" as a technique in the past. I think there's a lot of overlap between that model and the "puppy brain" label for limbic system activity. Thinking of this "second brain" (if reptilian is 1st and neocortex is 3rd - not talking about note-taking systems) as a black box, we can't see (be experientially mentally introspective on) what happens inside it, nor (this is just my understanding and current hypothesis) the connective neurons between the neocortex and the pieces of the limbic network. I guess it's only the stuff within the six-layer system that we can be conscious of. On Intelligence is a good book on that system, it's 15 years old but probably still worth reading.
We are complex distributed systems in every way. The elephant and the rider. Communicating, but (comparatively) poorly, even while being made of very similar stuff and connected by that same similar stuff.