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Left! Apparently it's only for passing even though I wasn't the only one driving in the left lane!

Last time I was pulled over (for driving in the wrong lane, there's a wrong lane? Who knew!) DPS Trooper first question was "sir do you have any firearms in your vehicle?" I told him .45 on my left hip and .45 carbine under the backseat, his reply was "OK" he asked for my license, I handed him my DL, LTC, and Security Commission, he handed me back the LTC, Commission, wrote me a warning, we talked about the Trooper that lives in my son's apartment complex and went our separate ways!
I see no reason to not present your credentials, if it will put them at ease, I'm good with that!