According to an article in the Korea Herald, people “vowed their heads” at a paying-respects site for the mayor of Seoul, Park Won-Soon. I hope not. Google found three other instances of “vowed their heads”, at least two of which relate to actual vowing of heads, and the third probably a error for bowed.
A seemingly self-published novel set in Norse saga times includes:
And therewith they vowed their heads for ever to the infernal gods if ever one of the blood brothers should desert the other, in danger or in need.
A very serious history of ancient Rome includes:
[S]o far did some strain in their expressions of their affections, that they vowed their heads and lives for [Caligula’s] restoring.
Another seemingly self-published novel set in fictionalised/fantasy medieval Roman Catholic Europe includes:
“We will serve you and your god, your holiness.” his servant vowed.
“We will all serve you master” affirmed by all while they vowed their heads before him.
Phonetically, it is more likely that a Korean will say or write bow instead of vow than vice versa, because there is an equivalent of b in Korean, but no equivalent of v; compare 비디오 (bi-di-o) for video.
The Korea Herald’s writer’s English is way better than my Korean, but she also refers to “a grassy plaza outside City Hall”. I would unhesitatingly write “the grassy plaza outside City Hall”, because there is only one grassy plaza outside City Hall. In fact, I would say and write “City Hall Plaza”, given that most of the Korea Herald’s readers know Seoul City Hall and its grassy plaza. The fact that the plaza is grassy is, in fact, irrelevant to this story.