"Healthy disrespect" for authority has a wide definition. Based on your question, I'm going to define it as "not accepting blindly what authority figures tell him, but not doing it in a way that explicitly defies the authority in a confrontational way". Basically, not automatically trusting authority figures, but not being a jerk about it.
First - I'm not sure it's a great idea to lie to encourage this. He'll figure out what you're doing, and that'll backfire on you. What you're doing seems like one good approach, though; just modify it from lying to him, to asking him to prove his statement, and asking "What about..." things that turn out to be wrong/irrelevant but make him question his approach. That's really the same thing, just without the lying. Lying to him is only going to make him distrust you, not authority figures in general - authority figures are very different from parental figures, in important ways: parental figures are much more inherently trusted as "safe", generally.
Learning to think analytically is the key here, though: and that's exactly what you're teaching him to do by questioning his answers. Not taking anything as given, but considering its source and its veracity. Push back on statements-of-truth from him, and he'll learn to do the same to you and other authority figures.
I have a child in roughly the same category - pretty similar level of math skills, almost same age. I have I suspect the opposite problem: helping him learn to respect authority figures in a way that is appropriate. He automatically disrespects authority figures, as he's confident he knows better than they do (myself included, for the most part). That's a big challenge with some gifted children: convincing them that sometimes other people do know more than they do.
For him, I try to talk through why people are doing what they're doing, and help him to think through their possible reasoning. This should be effective for children on both sides of the issue here; understanding why someone else says and does what they do is important for developing empathy, and for accepting why people might do things that are not what the child would prefer (assign homework, have a pop quiz, ask them to sit down, call on other children...)
Learning how to recognize someone who has a position of authority for a good reason is important, from both sides of this. A person should learn to take different inputs to determine how much respect is appropriate for a person: start with a position based on their authority level plus an uncertainty level, then lower that uncertainty level as they learn more about them and adjust the position accordingly. It's just like a statistical problem: define your prior, then test it using Bayesian inference.
Person: Calculus teacher. Prior: Likely knows math well given position.
First month, teacher effectively explains L'Hôpital's rule, seems to go into depth. Adjust respect up some, adjust uncertainty down.
Second month, teacher incorrectly grades problem set, acknowledges issue and corrects. Adjust respect up some (but be more careful with grading), adjust uncertainty down
Etc. ... and maybe the opposite if the teacher is not so good! If your child is able to understand this kind of thinking, then perhaps this is an effective approach to explain to him.
Finally - modelling is the most important thing I think you can do at this age. Model both how to correctly question authority figures, and how to give deference when it's appropriate. Talk about it afterwards if it seems particularly interesting.