Vagando means "wandering" or "roaming". It's a more evocative and less common word than simply saying "going" or "walking".
In the song, the singer declares, "Por tu amor yo iré vagando tras mi soledad" (For your love, I will go wandering after my loneliness). This paints a vivid picture of a heartbroken person aimlessly searching, driven by love and sorrow, making it a memorable and emotionally charged word.
The song opens with someone leaning in close, almost whispering: "Hey baby girl / Shh / Solo escucha" [Just listen]. Everything after that is the case he wants her to hear. He is not over it and he says so in the first line, "Por tu amor he sufrido tanto" [For your love I have suffered so much], but he never asks her to feel guilty about it. He just tells her what he has been doing with the time she has been gone. "Por tu amor yo iré vagando / Tras mi soledad" [For your love I will go wandering / Through my loneliness], and then the promise the whole song hangs on: "No descansaré / Hasta tenerte otra vez" [I will not rest / Until I have you again].
Halfway through, the wandering turns into waiting, which is a smaller and much more stubborn thing. "Ya sabes en donde estoy" [You already know where I am] is the most confident line here. He is not chasing her, he is staying exactly where she can find him: "Aquí estaré esperándote / Con todo el corazón" [I will be here waiting for you / With all my heart]. What he asks for in return is almost nothing, just one sentence out loud, "Así que ven y dime cuánto me amas" [So come and tell me how much you love me]. Alacranes Musical sing all of it over bright, galloping brass at a tempo far too cheerful for the words, which is a very northern Mexican way of handling a broken heart. The one big flourish he allows himself, "Yo viajaría hasta el infinito" [I would travel to infinity], lands because everything around it stays so modest.