No quick quenching. Quick quenching is only for hardening or tempering. Annealing is for softening the brass.
The case neck will either way cool relatively quickly. Brass is a good heat conductor so the heat escapes into the body of the case.
If you only heat the neck, the subsequent cooling of the neck will be too quick, and effectively it will become a neck hardening procedure, not an annealing procedure. So heat up both neck and shoulder.
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