For most of my life, I wore a watch (nothing fancy, traded out over the years) on my left wrist facing out. When I moved to SW Washington, I made a very conscious decision to stop worrying about time. The day I arrived here with all of my stuff, with just a tiny bit of ceremony, I removed the watch and dropped it in a kitchen junk drawer.
It's still there today.
BTW, I don't use a cell phone to check the time, either (cells don't work well out here in the woods). When I'm home, I use a wall clock; when I'm running around town doing errands, I use the clock in my vehicle. Being watchless is wonderfully de-stressing.