Moreover, there's the: don't think about an elephant right now => you just thought of an elephant, "problem". That is, the more you've been thinking about the problem a certain way, trying to force yourself to think differently only reinforces the original line of thought, leading back to the same local minima.
Thus, IMO the more likely mechanism that walking away from a problem and coming back to it later leads to a better solution, is more that you get a better random restart, and you have time to forget the prior line of thought, so you're more likely to think differently / explore a different branch of the search tree.
I don't think it's much like a minima, because I can go home, run some errands, cook dinner, surf the internet, read, etc, but when I'd come back the next morning I'd be just as stuck as the day before. For me it wasn't until I explicitly tried to do nothing (i.e. wander, as opposed to distracting yourself with other tasks) that I made progress.
(of course this is just anecdotal experience – not trying to frame this as The Way but found it interesting that there's some research about it)
This doesn't explain the many times (at least in my case, for example) where a solution pops into your head before you "restart." In other words, your mind seems to be working on the problem even if you're not consciously working on it / haven't consciously restarted.
Secondly, when the solution pops, my next thought is frequently "why didn't I think of this earlier?", meaning that the solution is quite obvious in hindsight, meaning had I just approached the problem slightly differently in the beginning, I wouldn't have to search very deep. So the solution didn't pop into my conscious thought because I've been mulling it over subconsciously, but rather the intrusive thought forced the problem back into foreground, but with a slight twist, and that quickly lead me to come up with the solution on the spot.
For intrusive thoughts where that didn't happen, I simply don't remember.
TBF, I admit I'm using a lot of weasel words, but I think it's possible to make my hypothesis more rigorous. Then you can design an experiment to falsify it, but I'm too lazy, and I'll leave that to real scientists. :-P