What is the etymology of the verbs 望む(のぞむ) and 覗く(のぞく)?
For reference, here are the (top) Japanese dictionary definitions. There are multiple for each one, but I only copied the top one for each.
のぞ・く : 物陰やすきま、小さな穴などから見る (source)
のぞ・む : はるかに隔てて見る (source)
I assume they share a common root. However, it's the origin of this "nozo-" root that has had me perplexed for a while. I don't know of any other native Japanese words that share this root. I thought perhaps it could be a combination of some の element + そく/そむ with そく/そむ becoming ぞく/ぞむ due to rendaku. But that also doesn't make much sense to me given that they're the only verbs that end in ぞく/ぞむ. (At least that I can find on Jisho).
In many words relating to eyes (and by extension, looking and seeing), the /m/ sound is present in the word/the verb stem (みる, まどろむ, まつげ, まなこ, etc), but it's absent in the nozo- root, which made me even more curious as to where it came from.
I've tried to search online for answers before, both in English and Japanese, to no avail.
Also, there's another verb, 除く, that is also spelled のぞく. Given that they're homonyms and share the same pitch accent pattern according to Wiktionary, I assume they're cognate. I didn't mention it because I'm having trouble seeing the semantic link between peeking through a gap/hole and removing/eliminating.
Anyway, any help or resources at all would be greatly appreciated.
Edit: Fixed a couple typos.