Well, your brain may in fact determine something is important but it won't fix your tunnel vision, it may not even allow you the impulse of checking what that is.
This is where consciously and unconsciously breaking tunnel vision is extremely important. Especially for LE (even though it can be translated into concepts for CCW citizens) given that 40ish% involved two or more contacts.
Dealing with a threat is extremely important, moving on quickly to scan and assess is just as important. Our eyes may betray us a bit in this context, we have to do our part through proper training to mitigate this.