In four quick lines, the speaker cheerfully admits that his words—especially his songs—rarely carry one fixed meaning. The parenthetical “(as the phrase goes)” makes the admission feel casual, as if he is shrugging at the whole idea of singing. Then comes the twist: if something he has said sounds both bright and true, he is glad to half-convince himself that he meant it. Notice the hedge in “I like to think I think I do.” He does not say he definitely means it; he only enjoys the feeling of believing he might. The mood is light, wry, and self-amused. It captures how people often discover or invent their sincerity after the words are already out, especially when those words are lovely enough to be flattering.
Songs About Life and Brighter Things Yet XLVIII — Summary
I seldom mean a single thing I say, or (as the phrase goes) sing; But if it sounds both bright and true, I like to think I think I do.