etymology - How are the noun 方【へ】 and the particle へ related?

I looked up the etymology of　古【いにしえ】 on gogen-allguide, and found the following:

いにしえは、「去る」を意味する動詞「いぬ（往ぬ）」の連用形「イニ」に、過去を示す助動詞「キ」の連体形「シ」がついた「イニシ」が、方向を表す名詞「ヘ（方）」を修飾した「往にし方（いにしへ）」。

This basically says that we take the verb 往ぬ, conjugate it, add the 助動詞 「き」, conjugate again, and finish by adding the noun 方【へ】. This was a bit surprising to me, since I've never seen the noun 方【へ】 myself, and was expecting the particle へ to show up there instead.

This is obviously suggestive of some sort of relationship between the noun 方【へ】 and the particle へ. So - what is the etymological relationship between the noun 方【へ】 and the particle へ?

Answer

Put simply, the particle へ is derived from the noun 方{へ}.

Bjarke Frellesvig provides a brief explanation in his book A History of the Japanese Language (page 132).

… The noun pye "side, direction" was being grammaticalized as an allative case particle pye, but in the Old Japanese period had not yet acquired that status.

As for pronunciation, sound changes would have likely proceeded something like *pye > *pe > *ɸe > *we > e.