I'm assuming that by "OCD tendencies", you do not mean a literal, clinical case of OCD. However, I think OP is describing OCD, the illness, not run-of-the-mill conscientiousness.
Despite the way it seems, OCD is not a rational illness, nor does it make you "better" at anything. It's purely emotional, and you can't reason with it. The sufferer feels a huge amount of fear/anxiety related to issues that seem insignificant to a typical person, and they can't choose which issues they are.
In fact, telling him that he makes more mistakes when he's more tired may give him greater anxiety, which would feed the vicious cycle of "doing more work to make sure I didn't screw up" that's going on in his mind.
