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As far as the best time, it's really luck of the draw. Maybe they'll be in a good mood on Friday afternoon, maybe not.
From my personal experience, I made two recon calls for the same product. The first was early on a Monday evening - a foreign female representative answered and was very short with me and declined me. The second was earlier on a Friday afternoon - a domestic male representative answered and was very personable and helpful and I was approved. I am male. I think what I'm trying to get at is, like all things credit, there is no "right" time and YEMV.