God the giver of doubt? God did not give doubt to humanity and nor is it a gift. The origin of doubt is within the sin of Adam and Eve when they believed the lie, doubted God (in His goodness, trustworthiness) and decided what was best for themselves.

The gift of reason, however, helps us discern according to truth, logic, morality, etc., and that can dictate what we accept and reject. But there is nothing in Scripture that says Jesus was exasperated over Thomas, not even in the original Greek. I mean, it’s one thing that Jesus was perplexed in the garden and sweat drops of blood, but to be exasperated is a specific term which means “ irritated or annoyed especially to the point of injudicious action” (sauce: https://www.merriam-webster.com/dictionary/exasperate#:~:text=%C9%99%2D)r%C9%99t-,1,exasperate%20seed%20coats) but it’s stretch to summarily use words and emotional expressions then attribute them to God in random places in Scripture. Injudicious is contrary to the holiness of God, even in the incarnation of Christ.