Annealing is temperature - time dependent. (see attached graph)
350 - 400 C will work fine if you maintain it for at least 10 minutes. The downside is the heat will conduct down the case and anneal that as well.
In a dimly lit room you need to see dull cherry.
Watch this metallurgist guy :
I gathered that guy is referring to a full anneal and recrystallisation when I saw it some time ago. As far as I know it is unnecessary for our purposes of case longevity but may be an advantage in constancy.
The idea of taking the cases to 400˚C is to stress relief anneal them i.e. to take them through the Recovery stage without going in to Recrystallisation temperatures. Stress Relief Annealing can be done at 250˚C if you hold a tonne of 70/30 brass for an hour.
Either full or stress relief annealing will work, the case will still hold a bullet whichever you do...consistency of hardness case to case is more important than actual softness. Stress relief annealing will prevent the case necks cracking and should be closer to the pre-exisiting hardness / spring back / neck tension.
The more stressed the metal the lower the temperature that recovery or recrystallisation commences.
But there is so much potential variation of outcome depending on the grain size that came from the original rolling and annealing regime of the billet before the case makers started forming it into a case, that possibly going for a full anneal each time would reduce the variation in resulting neck tension further, but it would be along with a reduction in strength/hardness.
Hitting the same temperature each time with a 400˚ C soap tell-tale is one way to approximate stress relief annealing constancy. The time it takes to achieve that in a gas flame means that it has been going through the recovery for a few seconds once it passes 250˚C.
If the metal was very stressed / work hardened, the recovery and recrystallisation will commence at lower temperatures. But the 400˚C is a reasonable sweet spot between them.
A gas torch flame varies by 1000˚C so the position the case is held in the flame can make a difference to the time it takes to achieve 400˚C so it is still important that the every effort is made to be consistent case to case with that heating time relationship.
Copper Development Association Cartridge Brass...

Hartman paper...
One can trade graphs 'til the cows come home but one of the papers I read put some of this nuance into perspective....the Norma brass study where they were trying to achieve the same outcome on their case neck hardness in production. They use induction heating to anneal between the various stages of drawing the cases and were surprised at the variation of hardness between different places on the neck, softer towards the mouth (duh! any metalworker used to heating stuff could have told them why!**)....and everything was going as expected until one day of testing all the samples were significantly different in hardness outcomes from the previous samples...they decided that to remove that glitch that they should have only used samples of cases made from the same coil of sheet from the producer!
Alan
**it is one of the reasons that the soap tell tale is more useful to us than Tempilaq. As the soap changes colour in the run up to 400˚C you can adjust the position until you heat enough of the shoulder so that it all achieves soap black at the same point. The case mouth, with less mass than the shoulder and no attached heat sink will always get hotter faster even in an induction heater as the Norma study scientists discovered. The effect is exaggerated with a gas torch flame because that is able to lick inside the mouth and heat both surfaces at the same time.
Hartmann
"Because of the possible commercial application of the proposed treatment of 70-30 brass, this work was undertaken. In addition, the data resulting from this work will result in a better understanding of the treatment of brass. The objectives of this work were as follows: Determine if higher...
scholarsmine.mst.edu
the Norma study