一眼之念
is an imitation of the structure 一A之B
. The structure usually works in the way of noun(B) of a noun(A)
:
一面之缘 Fate of an encounter
一饭之恩 Kindness of a meal-offering
一国之君 King of a nation
Personally I don't think 一眼之念
is a particularly good imitation. Because it would be interpreted as Longing of one look
, and like the English expression I've used, it is similarly unidiomatic and ambiguous. However, it's pointless to blame a pop song for being ungrammatical, and it's easily understood if we put it into context.
一念执着
is a shortened way of saying 一种执着的念想
. In English it would be An obsessed longing
or we could use a coma and write A longing, obsessed
. In Chinese it could also be 执着一念
. You asked about grammar, but in fact you can do all sorts of word play and ignore most of the grammatical restrictions in Chinese poems.
So to sum up:
一眼之念 A longing, result of one look
一念执着 A longing, obsessed
Not as beautiful as @NS.X.'s interpretation, but it might be closer to the original meaning.