In this lyric "隣で歌う声怖がりな背中を押して" I'm confused how the がりな背中を押して works. I know how 背中を押して is used thanks to this post. But what does 怖がりな note. Is the person or the action 怖がりな?
Structurally, 怖がりな must connect to a noun, not a verb. 背中を押して, despite being an idiom, isn't an atomic unit by itself; it consists of a noun 背中 taking the を-marked place of the verb (in te-form) 押して. Thus, 怖がりな modifies 背中.
If we describe the "back" that is being "pushed" (with the understanding that this is an idiom that describes encouraging a person) as "cowardly", it stands to reason that this is really describing (by metonymy) the person who needs encouragement.
怖がりな is the form 怖がりだ takes before the noun it's modifying.
The question then is what is it?
It is a relative clause, "who is a timid person".
怖がり could be either a coward or a timid individual. I decided, not knowing more context, to take a more optimistic approach (that the person is timid, not cowardly).
So, the lyric is referring to encouraging someone who is timid.