I shouldn't drink and listen to country music, period. Country normally doesn't do it for me, but "You were always on my mind," makes me think of people who ... were on my mind. The ones I never held like I should have, or told them I loved them as often as I could have. All of the things I should have said and done, and never took the time, but they were always on my mind. Anyway, it's one of my all time favorite songs. How much more sincere can you get? He's saying, "I screwed up and I know that. Now can I have another chance?"
Or, maybe I just sympathize with a fellow redheaded stranger. LOL