Absolutely, trigger discipline and muzzle awareness are the foundation. Thanks for your inputI was an RSO for 10 years at a public range and the biggest issue was trigger discipline.
Keep it simple. People can't remember more than a couple things unless they have some kind of super memory. That's why the 3 rules of safety are simple, and cover 99% of what a person needs.
Muzzle direction and trigger finger are what I start with. I pound the trigger discipline into new shooter's heads. Keep your finger completely out of the trigger guard until the gun is pointed at the target.