Mine is in the freezer, so I spend a lot of time buck hunting and just watching deer. That old saw about them having relatively poor eyesight is BS. I've had deer pick me out in light cover at 300 yards. With their eyes, not their nose. Old does seem to be the worst. They are constantly on the alert. They usually have fawns with them so that's more eyes to catch any movement. They can pick out movement really well especaiily horizontal forms like homosapians. I was "made" by a deer at over 250 yards while I was trying to get into my ground blind. But she was having a hard time deciding what I was and started to approach for a better look. She lost interest when I slowly got down and started to crawl very slowly on all fours at right angle to her, pausing often in the process. Took me a while but I got to the blind without blowing that bunch off the field.Their hearing is most acute as we all know. The other day I tested it by opening a can of pop while deer were picking corn stubble some 250 yards away. They picked the sound up instantly. I didn't actually open the can, just made that initial light metalic pop and fizz. They knew it wasn't "woods sounds" and exactly were it was coming from. I have no doubt they can hear a safety going off far further than yours apparently did. BTW, I had a three position safety put on my rifle just for that reason. It makes a click going form lock to safe. But not from safe to fire. So I walk with it on lock, but it's on safe in the stand and comes off silently, with only 1/3 as far to travel than before.
But one can make sound work in his favor. I shot a big ole doe with my X bow recently that was focused on a corn combine. In fact she didn't even run after the hit. Must have though it was something to do with the combine. When the combine showed up I though my hunt was over. Actually, the deer were not afraid of it, they came out to feed but kept watching it when it was close to them. Combine operator said they let him get pretty close at time. Hmmmm.