How do you "outsmart" Gil, though? He seemingly has the ability to just look at someone and work out what they're thinking....
Also, the problem with Gil is that it's difficult to fail at first and succeed later, unless you have something up your sleeve that he's not aware of. Once you've fought him once, he's less likely to underestimate you the next time.
Gil will almost
always underestimate you. If you bring out something he doesn't expect, you'll catch him off-guard. And because of his ego, you have a lot of room to work with. Sure, Shirou may not have been
trying to outsmart him with UBW, but Gil certainly underestimated the "mongrel", and thus got himself into a corner.
And, well, Gil's supposed to be "endboss" material. You usually don't need more than two confrontations with him to set the point (Too OP, can't beat; suddenly EUREKA moment; rematch using that knowledge and hero wins)
Outsmarting him is flopping out of the fight. Narratively it only works once anyway. In the original he had ways to beat him that weren't repetitive tricks and, again, one of the major reasons Gilgamesh is even in the story is now impossible to carry forward. So there's literally no point to Gilgamesh being present in the reboot.
Um, just pointing out, but even Gil has a limit, and if you constantly beat him, he *will* eventually get desperate enough to pull out a perfect counter. And, if that fails, he will probably rather Ea you rather than having to deal with you anymore. Sure, that may have had to do with his role as stealth teacher as you mentioned, but I'm sure the characters
would find Gil's behavior odd, given his attitude I mentioned above.