Bean, the expression, "It was the last thing on my mind" implies to me that the person wasn't thinking about the subject at all. If something were the last thing on a person's mind, it would be on that back burner in the brain -- the one way back there where the unconscious brain is a bubbling up its trouble.

But you wrote that the lyric was "You're the last thing on my mind" -- and that is present tense [are] and that suggests that very cool ambiguity you sense, and I do, too. If something is the last thing a person thinks of, "You are the last thing I think of before I go to sleep," then that something has come into conscious thinking. But when you throw the subject into the phrase that means not to think of something at all, i.e., 'That was the last thing on my mind,' and chuck the whole phrase into the present, 'You are the last thing on my mind,'--well, there's the ambiguity. I like it. I like the ambiguity here--like it a lot in lyrics and poetry. Wish I had all the words to look at to get a sense of whether the ambiguity is in line with the lyric you've given us here.

Guess I'll go google Barenaked Ladies now..

Best regards,
Wordwind