Having no definition, I'm a nonbeliever.
Then what is it that you are not believing?
But given I think I'd need to withhold belief from something coherently described and claimed to be real, and not just something as trivial as 'imaginary', I have no so such definition, and I seriously doubt one exists.
You are becoming very confused, here. The theist proposition is that God/gods exist. The question being posed to you by this proposition, then, is what God/gods exist, how? And you are trying to respond with "I don't believe you", which is an incoherent answer, as it was not what's being proposed. What is being proposed is a conception of existence that includes God/gods. What you believe or do not believe about other people's conception of God/gods is not relevant.
I'm all in favor of love, kindness, forgiveness and generosity. But please explain what you mean by 'divine' here, and why those particular traits seem to you to fit your definition. Or is 'divine' meant to reflect a personal approving attitude in the speaker, rather than any quality of the trait itself?
I understand these to be "divine characteristics" because they transcend the mechanisms of physical existence. They are metaphysical, i.e., "divine" phenomena. And through them existence becomes more then physically extant, it becomes valuable.
The best answer I can give you, after thinking hard and debating my ideas on the net over quite a few years, is that 'a god' or 'God' is first and foremost an imaginary being.
"You" and "I" are also imaginary (metaphysical) "beings" that exist only as a cognitive experience within a human mind. And yet you would not deny that we "exist", would you? 'Love' is also a phenomena that exists only as a cognitive experience within a human mind, and you would not deny that love doesn't "exists", would you? 'Truth' also only exists as a cognitive experience within a human mind, and yet you live by this ideal every day of your life. So why is 'God' less extant to you then these?
In the Abrahamic West he's often conceived of as being able to do everything, and as loving but with a stern side, so perhaps he's like a huge version of the way our fathers seem to us when we're four.
Perhaps. But why are you critiquing someone else's conception of God? It won't change their mind, nor should it. And it won't illuminate yours. So what's the point? Why not ask yourself the real questions being posed to you by the theist proposition: what God/gods exist, and how so?