Agree with the advice from lock man. Enough things have been happening in your tank already that you won't see the simple idea you first described of seeing some ammonia readings and then seeing some nitrite readings. Instead I agree with lock man that you'll probably just have persistant amounts of nitrite(NO2) over some period of days or weeks which will then finally go away to what we call "double-zeros" (meaning zero ppm ammonia and zero ppm nitrite(NO2) when you test.)
On the Nutrafin liquid tests, 0.30 is the equivalent of the first color indication just like 0.25 is on the API tests. So we consider that to be the maximum of either toxin that you should have, the "gate" so to speak, which should trigger you to change water again (if you've hit it or are getting close to hitting it.)
Your job as a fish-in cycler is to figure out a pattern of percentage and frequency of water changes that you can manage based on your daily schedule and how fast you see the toxin trying to come back and hit the gate (0.30ppm.) Usually people test twice a day about 12 hours apart (test ammonia and nitrite(NO2) since they can come back on you despite seeming steady at zero for a few days) and only ease up on this when it's obvious it takes all day for a little to build up. Often the nitrite will just sit there at 0.25 or 0.30 and go like that for a very long period before finally being 0.0 one day.
When you can go two days without changing water and it stays at double-zeros you know you are ready for your qualifying week, so you just see if it keeps this up as you fill out a week of days with double-zeros, after which you consider the filter to be cycled (which means you can wait a couple more weeks and then do an addition of two or three fish if that's what you're waiting for or you can ease off the testing and water changing if that's all you were waiting for out of the "being cycled.") Does that make sense?
In fish-in cycling you learn to never hesitate to do nice deep gravel-cleans along with the siphoning out of lots of water (the toxins are invisible and contributors to this hang more within the gravel, so it's not all about seeing debris.) The re-fill tap water should be conditioned (at 1.5x to 2x whatever the instrucs are but not more than 2x) and roughly temperature matched (your hand is good enough for this.) After you are cycled, this process will be second nature and your weekly water change habit should be a snap! This keeps your fish used to the characteristics of your tap water, allowing the tap water chemistry to serve as a wonderful emergency backup for all problems that may occur in the tank in the future (in other words, when in doubt, water change!)
~~waterdrop~~