Yes, the fact that once you were finally able to get enough of that weak ammonia in there to get the tank concentration up to 5ppm and then it dropped to zero ppm in 12 hours, means that half of the biofiltration is working properly. The nitrite processing half is also nearly there, just showing a trace of nitrite 12 hours later, right?
So once the nitrite drops completely to zero ppm within 12 hours after the next dosing of 5ppm of ammonia, you will have started your qualification week. The test we have for whether the mini-cycling is going to come back on you is to watch it perform for the better part of a week, usually the week during which you are figuring out which fish you are going to add and whether they will be available on the weekend coming up.
This is a good test because sometimes it will surprise you and you'll get a spike in one of the poisons or the other, something you would not want once you get fish.
~~waterdrop~~