How This Thing Works (as of late October 2022)
Thank you to User:ARCHSENEX for the explanation of how the auto-perfumer works.
TLDR: Keep your auto-perfumer at T2 if you want to use permified perfumes with it unless you don't care about losing the actual bottle of perfume.
It's important to understand that, as the auto-perfumer is currently designed, you will lose your permified bottle if your auto-perfumer is at T3+ levels.
The best way to think of the use of the auto-perfumer is if you want to randomly rotate through a handful of perfumes, and want it to auto apply every 4 hours without you having to mess with it. Everything else is extra functionality.
Let's say your auto-perfumer is a T2 that can hold 50 charges of a perfume. Let's say you have a 110 charge bottle of perfume.
When you SHOW the auto-perfumer the bottle you will transfer 50 charges from the bottle to the auto-perfumer. Now the bottle is down to 60 charges.
Let's say your auto-perfumer is down to 10 charges and you show the bottle to it again. You will transfer 40 charges. Now the bottle is down to 20 charges.
Let's say you do this again at 10 charges. You will transfer 20 charges. Your auto-perfumer will be at 30 charges and the bottle, now empty, will be destroyed.
If you were to do this with an unlimited charge bottle you will transfer up to the max the auto-perfumer can hold, and because the bottle is unlimited, it will never be destroyed.
However, at T3 the auto-perfumer can now interact with permified perfumes. When you use a permified bottle the auto-perfumer will set the perfume in it as unlimited and destroy the bottle in the process. You can achieve this same effect at the T2 level by continually adding charges to the auto-perfumer and also retain the permified bottle in the process. The drawback of the T2 compared to the T3 is that you have to keep an eye on charges at T2.