Let's not have this debate again. I'll accept that this is the definition that you will be using. That also means that we can't go very far, but that's now your choice.
If you want to talk about something other than a supreme being, then you should probably use a different word than "God". Just like when I want to talk about horselike creatures with black and white stripes, I use the word "zebras" instead of "shoes" because that's the best way to communicate.
First, I don't think you use reason as doggedly as you do in this instance. I think, like most people, you will believe what you consider to be a trustworthy source until the issue or topic comes to be of higher importance.
Sure, but that's reasonable. It also depends on the claim being made. If the claim is that there are 500,000 atheists/agnostics living in New York City, I'll buy that, at least until I find out differently. That's partly because it doesn't really matter to me, and partly because it's not a very outrageous claim. Now, if someone claimed there were 5 million atheists/agnostics living in New York City, I'd disbelieve them unless they came up with some good evidence.
But really, the point is, if you're trying to figure out the truth of a claim, the only good way to go is through reason. All you're saying here is that many times we don't even bother trying to figure out the truth of a claim (as in my first example).
Second, we are not talking about what I believe here. You believe that the idea is to reach truth. I will agree with that. What I do not agree with is that, in order to reach truth, you must use rational methods.
I do not go 'flitting about believing things willy-nilly on a dart toss'. As I said, there is a difference in believing what you want, and letting life tell you want to believe.
If you're using irrational methods to try to reach truth, you're doing the equivalent of throwing darts. It's possible to end up at the truth through irrational means, like faith, but it's unlikely. It really is like trying to hit the bull's-eye. You can use irrational methods like closing your eyes and throwing backwards, or you can use rational methods like looking at the dart board, focusing and throwing straight ahead. Either way, it's possible to hit the bull's-eye, but I think you'd agree that the second way gives you an immensely better chance of achieving that goal than the first.