How do you determine its a miller trigger or other brand?

A Miller trigger will normally have the word MILLER stamped into the side of the trigger. Sometimes it is almost or even completely obscured by the trigger plate and you may only be able to see the edge of the first or last letter.

I have had lots of guns with Miller triggers, two here have the Miller name stamped on the right side of the triggers installed in the 70s and 80s. A more recent (2002) Miller installed at the Turnbull shop has the Miller stamped on the left side with the Turnbull insignia underneath it.

Since the Miller company has changed hands a couple of times in the past 12 years the price of the trigger is up there almost out of reach of the average shooter, I think.

Where is your selector located? The earlier Miller selector is in the safety button. The later Miller selector is a rocker in front of the trigger.

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Weren't there three Miller designs?

Howard Miller would ask me every time I sent a gun to him if I wanted the newest design or the same old one. I have at least two of the designs here, the safety barrel selector and the trigger guard selector. Miller had an option of an automatic safety on or not. He also offered to place the trigger where the front trigger used to be or at the rear trigger placement. I don't recall having an option of the trigger guard placement. It just happened and it was right after Howard sold the company to Turnbull. If I had the option, I would have opted for the safety design. The trigger guard selector can be moved when the shooter is wearing gloves without the shooter knowing the barrels have been switched.

The rocker style selector was in production for many years when Howard sold the company to Doug Turnbull. The trigger mounted trigger patent was 1962.