phorwath, roughly how many rpm are you spinning your cases in the hand held drill? or how many revolutions is your case making in the 5 1/2 seconds?
The Lee Case Trimmer shell holder and assembly securely holds the rim of the cases by screwing the shell holder onto the piloted base plate. The shaft on the base plate is chucked into the drill. End result is the case can be spun concentrically at high speed with very little wobble, allowing one to keep the neck-shoulder joint in the focused part of the propane flame.
Answer to question: I spin the case maybe ~200 rpm. The whole point is to ensure all sides of the case are exposed to the heat uniformly. So if you spin the case say - 3X per second - that should be sufficient to apply the heat uniformly.
The uniformity of the applied heat to all sides of the case and the ultimate temperature the neck/shoulder joint the brass is heated to are the two key points to good neck annealing. The idea is to bring the case neck brass up to temperature quickly, before the case head has time to get hot. Then quench the case in cold water (I use ice water for uniform temp of 32F) quickly so the heat doesn't ever reach the case head area.
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5 1/2 seconds. Logically the time to keep the case neck-shoulder joint in the flame depends on the temperature of the flame. I use a standard propane torch. I adjust the flame so that the focused deep blue flame is 5/8-3/4" long. I steady the drill with both hands while seated at the kitchen table, with a large second hand clock in the background. Hold the neck-shoulder joint (maybe a bit more on the shoulder than the neck) at the tip of the deep blue flame (about 3/4" from the mouth of the torch) for 5 1/2 seconds. No more than 6 seconds. Quickly submerse about 3/4 of the forward part of the case in the container of ice water to draw the heat off the case before it travels back to the case head.
Eaglet mentioned don't heat the case neck/shoulder of the cases above 750F. The ideal annealing temperature is about 660-670F. The cases have already been overheated by the time they begin to glow red, based on my research and understanding. Over-anneal and the brass turns to a charred soft mush. Useless. Toss'em in the trash. Under-anneal and the brass is never softened up.
There is some lattitude surrounding the ideal temperature, which allows the annealing to be done successfully by the handloader if care is taken during the heat application process. But too low of a temperature doesn't get the job done and too high destroys the brass.
NEVER heat the case head area. Annealing softens the brass and you'll destroy the brass by heating the case heads any higher than ~450F, because the primer pocket will then expand under high pressure and you'll get a face full of 60,000 psi gas in the face when you pull the trigger.
PS: Anneal with deprimed cases. That way when your hot cases are quenched in the cold ice water, they blow less hot air into the ice water bath. Also easier to shake the majority of the water out of the cases without the spent primers present.
PS2: If you're reaching the correct temperature, the heated area of the brass will have lost it's luster, yet not be cooked too dark in appearance. They will look similar to Lapua case necks in color, or Lake City brass that have been annealed at the factory.
PS3: I've read about the lead dipping annealing process. Molten lead is the ideal temperature for case neck annealing. From what I've read, I decided not to even try it. I just didn't want to deal with the health aspects of breathing lead fumes without having a fume hood, and the risks of messing around with a pot of molten lead. It's the ultimate heat source for annealing, but I personally would start over with new brass before performing the research and then purchasing the equipment to set up to safely anneal with molten lead.