I do the same .... towel/rag hanging out of my back pocket. Its automatic now, and never leave home without it. :-)
I adopted the 'rag in the right rear pocket' when I started working at age 15 for Red Mayfield in Santa Clara, CA.
"Mayfield's" was the 'best damned garage in town', and the rag became my banner. I always had one on me when flying, it was 'dress code'.
My wonderful wife, Joey, laughed once when we were going somewhere..."Aren't you forgetting something?" we laughed...
After I retired from the business, I was still doing some specialty jobs at home.
Joey puts on a Safety banquet for 160+ Foster Farms big rig drivers every year, very 'posh'. Last year when we got dressed, I wore a black single-vented suit, with coordinated shirt & tie...I hung a red rag out of my back pocket to make her laugh, but she didn't notice, and I forgot.
We greet the drivers and their wives at the door, and when Trevor Foster, the owner, came up he asked, "Checking oil tonight, Mike?"
I looked down, and he had the end of my trusty shop towel in hand...Then I DID get a laugh!