Yes! Considering that the same thing happens when I take a shower (sometimes) and when I meditate (usually), and that both of these are vertical in nature (usually), I think it's primarily to do with letting your brain 'rest'. Mindfulness and all that jazz.

I don't know what your life is like, but for me that's definitely the most likely explanation. When I'm not showering, meditating, or horizontal in bed, it usually means I'm reading something, watching something, working on something, or engaging actively in an internal monologue (that usually is more about reducing variables and maintaining control or the illusion of it, and less about creativity).

The moment my brain gets some free time, and there's nothing acute to worry about, ideas start to appear and I get excited.