Amanece means 'it dawns'. It's a fascinating verb that captures the entire concept of sunrise in a single word, a common and poetic feature of the Spanish language.
In this classic ballad, Juan Gabriel sings that he remembers his love 'cuando amanece y anochece' (when it dawns and when night falls). This beautifully expresses that his thoughts are with this person from the very beginning to the very end of each day, showing a constant and unending remembrance.
This is a song about a memory so powerful it takes over everything. Juan Gabriel, a legend of Mexican music, sings about someone he can't forget. He sees this person everywhere, in all of nature. He tells them, "Te recuerdo en cada estrella siempre que aparece" [I remember you in every star whenever it appears] and "Te miro en cada flor que al colibrí se ofrece" [I see you in every flower that offers itself to the hummingbird]. The memory is tied to every moment of the day, from when the sun rises to when it gets dark.
This constant remembering is both a comfort and a kind of madness. The singer calls the thought of this person divine, because in his mind, he can see, hear, and hug them, feeling that they never left. But he also admits that this obsession might be unhealthy, singing, "Aunque de tanto, y tanto pensar / Yo voy a parar en loco sí" [Although from thinking so, so much / I am going to end up crazy, yes]. It's a beautiful and intense look at how a person can live on inside you, long after they're gone.