おぼつかない describes something shaky, unreliable, or unsure, often like steps that might give way. In the song, the night feels uncertain and the music seems about to stop, creating a dreamy, vulnerable mood as the singer wants to stay with the other person despite not knowing what comes next.
NIGHT DANCER is a late-night slow dance in song form. It opens with "どうでもいいような 夜だけど" (it's a night that doesn't really matter), and that shrug is the whole point: nothing special is happening, just two people in a messy room they've spent way too much time in, with a record playing. The details are lovely. There's "散らかる部屋" (the cluttered room), a song they played "聞き飽きるほど" (until we got sick of hearing it), and a record needle that keeps stopping and getting dropped again.
That needle (針) is the clever bit. imase uses it as a clock hand too, so "刻む" (to tick, to keep time) pulls double duty: the record keeps the beat while time keeps moving. When he sings "二人刻もう" (let's keep time together, the two of us), it means both dancing in rhythm and marking the hours together. Meanwhile the couple are awkward in a sweet way, dodging with "無駄話" (pointless chatter) and hesitating before they touch, until their breathing starts to line up.
Then it gets a bit dizzy and romantic. He wonders if staying unchanged is possible only "今だけ" (just for now), sips coffee to calm a floaty heart, and admits "君といたい 溺れてたい" (I want to be with you, I want to drown in it). By the end he doesn't even care if tomorrow comes, and the last invitation is to keep dancing "ふらつき よろめきながらも" (even while swaying and stumbling). Language tip: notice the rhyming pairs like 響めき / 煌めき and ときめき / 色めき. They're all -めき nouns describing a stir, a sparkle, a flutter, and they give the chorus its bounce.