Confirmation bias is related to the tendency to say that all of the evidence is on my side. In particular it consists in attending to evidence that supports my position while ignoring contrary evidence, or interpreting the contrary evidence so that it appears to be supporting evidence. One way to resist this tendency is to notice that despite the saying, absence of evidence is in fact evidence of absence. If observing some evidence tomorrow would make your hypothesis more likely, then if tomorrow comes and you do not observe the evidence, your hypothesis becomes less likely. So if you can recognize the circumstances in which your hypothesis becomes more likely, you should be able to recognize the circumstances in which it becomes less likely.
For example, in the previous post, most people would recognize that (2) is evidence against (1), but recognizing this appears to be more difficult for Mormons. Nonetheless, if it had turned out that the Book of Abraham was in fact an accurate translation of an ancient Egyptian manuscript, this would have been evidence favoring Mormonism, and there can be no doubt that Mormons would have recognized it as such. Consequently, if they can recognize that this would have favored their position, they should be able to recognize that the actual fact (2) is evidence against it.
You cannot have it both ways. If you concede that getting what you ask for every time you pray to your guardian angel would be evidence for his existence, then not getting what you ask for is evidence against his existence. Of course such negative evidence is not necessarily very strong, and this may in fact be the point of the linked post.