Tired Bunny
When I get sleepy, I do something that I used to find moderately embarrassing, but having been indulged in it by M for nearly two years, and R for two years before that, I now find it somewhere between relaxing and a moderate inconvenience.
When I'm sleepy I get very... Bunnylike is what I'd like to say, but infantile may be closer. I just make lots of small, incoherent sounds, curl up and want to snuggle whatever is closest to me. I lose the ability to comprehend large concepts such as speech or decision-making, and gain an inordinate amount of love for fluffy objects.
Nuzzling, clinging and wordless vocalisation are all on the agenda, and I become more or less a puddle of useless, but hopefully cute, goop. If you show me literally any affection or kindness I will get very snuggly and make quiet, grateful sounds.
It's actually very pleasant to indulge in when it's safe to do so, and I imagine it's somewhat like subspace. Then again, it might be subspace, I don't know. I've not really ever thought about it that way. But it definitely requires being around someone willing to take on a more dominant, caring role for a little while, as I'm liable to trip over my own feet and fall over a lot when I'm in sleepy mode. But sometimes, when someone is willing to do it, it's very nice to be looked after for a little while.