I'm playing an artificer/warlock in a setting inspired by Han dynasty China. My character has taken it upon himself to essentially invent science, and happens to have access to all scientific knowledge through his Patron. (For reference, during the first session I happened to meet the most qualified contemporary doctors, who were treating poison with the finest incenses and ointments. The other sciences are in similarly poor positions.)
My current strategy is to start a cult of science. The Illuminati seem to be the best example for me to follow, since there is a decent chunk of science that is either heretical (e.g. earth is a Sphere, the nobility is dangerously inbred for no reason) or dangerous (genetics being the foundation for eugenics, fission/fusion being the foundation for nukes). Restricting these things seems pragmatic, and the traditional lodge structure gives a good framework for this.
So, this comes down to the question of which knowledge should be restricted, to what degree, and what traits should be tested to determine worthiness. What knowledge do you think is dangerous? And how do you think i should I test worthiness for that knowledge?
If his goal is simply to preserve the superficial practice of scientific technologies, a good inspiration might be "Scientism" from Asimov's Foundation.
If his goal is to keep powerful knowledge out of the hands of all but those who understand it well enough to use it responsibly, then yes you'll need some "initiation" or "trials" to select promising minds, and some concept of forbidden knowledge. Since your character is the bottleneck, it might be more productive to ask which knowledge shouldn't be restricted.
Ultimately, this is going to depend on your setting. Generally speaking, you have to take into consideration how powerful a piece of knowledge is, and how easy it is to implement. Powerful knowledge that requires complex technology to utilize (e.g. genetic modification) isn't much of a threat, and will be dismissed as legend more often than not. Weak knowledge that's easy to utilize (e.g. hand washing) likewise isn't much of a threat, and can propagate freely. The same applies to weak knowledge that's hard to implement, only crackpots will bother trying and won't accomplish much. Those crackpots might, however, be a good initial pool for candidates, since they're willing to put in great effort to sate their curiosity for little material gain. Further culling is necessary though, since some might just be crazed.