This is a very opinionated question, so I don't know how much I can help, but as the babysitter of four kids around this age- I would suggest telling Timothy that he can take a nap if he wants, but he still has to go to bed early- (8 or 9 or whatever.) he doesn't neccesarily have to sleep, but he does have to stay in bed quietly and not disturb his mother. (my family does the same thing, they're allowed to read or talk to each other quietly if they're the 2 that share a room.) Likewise if he doesn't take a nap and becomes grouchy, he could be "punished" by going to bed earlier, which may end up helping. Timothy might be agreeable to not taking a nap because you could frame it like him being a "big kid."
You could also just make it so his naps are shorter, and wake him up on your own instead of letting him sleep for a full 2-3 hours.
one of them is "there once was light but now there is darkness."
