Hmm, (just going to piece together my thoughts in the comment to build on a answer xD)
The way the brain processes thought:
A range of sensory inputs to the brain.
Our freewill which can be described as dynamic mental adaptation to current events.
Memories that sum up the history of sensory inputs on a fundamental level.
The piecing of sensory inputs together in some shape or form through freewill, but since our enviornment does not require us to actively survive it gives us the luxary of thought on other things that we will to think. . .
Common knowledge Biases that could be mistaken as assumptions:
Humans are not different to other living things in being able to observe reality only their senses.
Self reminders of word meanings:
Consciousness-
noun: consciousness; plural noun: consciousnesses
the state of being aware of and responsive to one's surroundings.
"she failed to regain consciousness and died two days later"
Nature-
noun: nature; plural noun: natures
the phenomena of the physical world collectively, including plants, animals, the landscape, and other features and products of the earth, as opposed to humans or human creations.
"the breathtaking beauty of nature"
In this regard every living thing with senses has a consciousness when viewed without a species bias.
Observation of reality is also observation of self by our senses or reflection of senses.
Q:
So, I am asking what does thought tell us about the nature of personal identity and about the underlying source of consciousness? Do thoughts help to explain the nature of consciousness? — Jack Cummins
A1: Thought is a translation of senses of reality to the brain, because we are able to sense ourself that we are being in this reality, our very identity. Conciousness itself is a combination of our senses and free will with memories being a type of subconcious being able to recall it.
A2: The nature of conciousness is to act in response to reality through senses, This acting or responding to reality based on senses is freewill. (Since this answer itself is a thought, it itself answers your question.
;))
Note: The fact we are able to think about such random things is because we have a history to create and learn from, the evolutionary advantage of physical creation, while not having to actively fight for survival.(in some parts of the world)
You could say we are the ultimate day dreamers of creations.