My experience with it is that you can both let it hang on the tree until its ready to drop (in which case it will take on a unique flavor in the vinous spectrum, along with mellowed acid) or pick it earlier and store it which case it gets sweeter and mellower but not with the same complexity as letting it hang on the tree a little longer. Even when picked when they are ready to drop, they will store well into Spring. In my location, I would view picking in mid-November too early unless you were aiming to pack them away for something to pull out of the fridge as late as possible. They are a treat now, both for eating and baking, but I usually pick mine around a week before X-mas. I've not encountered the flavor it takes on when fully ripe in other apples--its a "darker" and not particularly "applely" flavor; if you like that, I suspect that you will like Hauer a lot.
At least in my location, I think it's an underappreciated apple: The tree is an unstoppable grower, is free from disease, and consistently produces good crops; the fruit is large, virtually free from blemish even hanging on the tree X-mas day, and good to very good from now until the start of May under refrigeration.
Comparing it with GoldRush, Cripps Pink, and Arkansas Black (which is the limited set of good late keepers I have to use as a basis for comparison), it beats Arkansas Black in all eating qualities; Cripps Pink is a little crunchier late into the Spring than both Hauer and GoldRush for me; Hauer, GoldRush, and Cripps Pink, have roughly comparable quality and intensity of flavor and it's a matter of mood and personal preference come Spring. I say that with the caveat that I don't think that I have figured out how best to grow GoldRush yet. My personal ranking is usually Cripps Pink, Hauer, GoldRush, FWIW.