So, the way I see it, I can pretend we haven't figured it out and thereby avoid committing our resources and - to the extent things are zero-sum between our hosts - harm you, or I can admit I've figured it out and then start helping even though this will probably make my reputation for untrustworthiness even worse. And I'm going to do that, because I want the Enemy dead very badly.
Or you could tell us and we could spend the research time on something else, but I'm not sure the research won't be fruitful even to the extent it doesn't bear on this specific secret plan of yours, and we'll probably accomplish about as much magical-research-wise in the next year whether we're hunting down your secret or not. I am assuming it's not reproducible from the effect, or the Enemy can do it, but it's also not tremendously complex because it's not in your domain of specialization and you don't know much else that is complicated and you're not bottlenecked by training people to do it. I can brute-force that in a year, the way my people work.
So the only advantage to telling us now is that we can start helping sooner - and, I guess, that we can't admit we know it and offer our help at a time convenient to us - but it certainly seems that the only disadvantage is that you don't like us, unless I am to conclude you're planning on picking a fight with us in the next few years.