What I'm asking you to do comes down to believing, in the absence of evidence, on my say-so.
You haven't asked me to do anything. And while you may be enamored with Mr. Sagan, his invisible dragon is basically infantile logic for sloppy thinkers.
I don't know and I don't care about your dragon, and I have seen no reason from you how this is pertinent to our discussion. If your invisible dragon is supposed to represent God, your analogy is incorrect, for your dragon could represent "thought" or a "black hole". With this sort of thought experiment, your "dragon" must be a faithful representation of God or your entire thought experiment is bogus.
It is silly to require physical evidence for something nonphysical. It is like doubting the existence of black holes because you can't see them. Physical things can be proven with physical tests. Non-physical things cannot.
what's the difference between an invisible, incorporeal, floating dragon who spits heatless fire and no dragon at all?
Well for one, you wouldn't be sprinkling powder on your garage floor if there was no dragon.
The actual logical error Mr. Sagan makes is that he assumes that the "dragon" not being detectable by physical tests, is the same thing as the "dragon" being unable to affect the physical world. There is no logical reason for that assumption. It is a leap of logic.
Mr. Sagan misses the most logical question because of his bias, that even a high schooler would figure out.
Ask the claimant how he became aware of a fire-breathing dragon living in his garage!
This "experiment" is akin to placing a person through multiple brain scans to find out if they are thinking instead of simply asking them if they are thinking! But the "trick" in this thought experiment needs the multiple failed physical tests to divert from the obvious question not being asked.