This is a good time to assess whether you are ready to 'believe him when he tells you who he is'.
He is telling you ‐in words and actions- that he is a person who requires considerable downtime during which communication might slow, needs to recuperate a lot through sleep and isolation, experiences low moods and shyness.
This is eliciting a response in you; you want to 'get it right' and you believe your actions might cause him to feel 'pressured' and like he needs to retreat.
Pause and ponder. He is the expert on his needs. This is how he ensures they are met. Good for him.
Only proceed if you are 100% at ease with how this feels to you now. As in 'very comfortable indeed', and that it will not cause you to second-guess your spontaneity or gut-feeling or emotions. That it will not cause you to compromise on your own feeling of comfort and ease as you try to make things right for your friend to avoid unsettling him. Because any feelings of insecurity and uncertainty now are likely to linger and remain as your connection deepens ‐not diminish.
What are you like? If any part of you enjoys carefree expression and spontaneity, or honest addressing of differences of opinion or expectation as issues arise without needing to cautiously curate the delivery, really think about whether to take this further. If you too have times when centering your own needs feels important, or your expectation is one of mutually doing any 'heavy lifting' as far as relating and communication is concerned, proceed with caution. Because what nourishes you is also important.
Our loving relationship should feel like calm havens, spaces of mutual understanding and relaxation. They shouldn't be hard work as a baseline, with rewards of goodness and respite as a result of 'getting it right'.
Whether a romantic partner has social and communication differences, as with ASC, or just communicates and engages with the world in ways which are different to yours ‐and especially if the stakes are raised by high-impact consequences such as overwhelm and withdrawal‐ the course of a relationship can be very challenging (for both parties). It's rarely a case of 'it was tough but we got there in the end' as the differences are hard-wired; you can't rely on 'learning your way out of them' or hoping to make sufficient adaptations, or in the case of the ND partner, de-sensitising sufficiently -the differences are built-in and although we can learn strategies to cope better, they won't go away.
Nobody's love is special enough, nobody's attention to detail, or commitment to meeting a partner's needs is fine-tuned enough to guarantee an easy ride with challenges to the baseline of communication and interaction like this.