^ OP talks about subject in the grammar sense, which in Japanese is often omitted
I think the subject in the first verse should be "I". My understanding is this:
Just after I said "See you tomorrow" with a smile without much thought
I realized I have you here to say "See you tomorrow" to me
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Mit der Dummheit kämpfen Götter selbst vergebens.
Against stupidity the gods themselves contend in vain.
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