When I started with the U.S. Forest Service I used to drive a patrol engine. The FS required fire people to be on a tour with a one hour lunch even though most of us would have preferred a half hour, allowing us to go home earlier. But an hour lunch kept us available longer without additional funding so they made us do it. I used to find a secluded spot to have lunch where my rig could not be seen by the public. I would eat lunch in 10-15 minutes, then lay my head back on the seat and sleep for 45 minutes. Routine traffic did not wake me up, but if my unit number or smoke sighted traffic came over the radio I would be awake in a second, mike in hand, and speaking completely coherently. I never overslept either, the truck was started up between 50-58 minutes after I started lunch without fail.
On public contacts either on foot or while in a vehicle you become used to speaking and listening to the person you are contacting while simultaneously listening to a radio turned down a bit low. If you can't do this you either can't talk to the public very well or you miss a lot of important traffic on the radio. As a supervisor I not only keyed in on my own unit designator, but those of the people on the ranger district I worked on, and even more closely those I supervised. Almost anyone can do this, it just takes time. "Necessity is the mother of invention."
With scanners now, my wife cannot understand how I can work in my home office with three of them and two ham rigs going all at once. Sometimes she will ask me for clarification on some of the traffic and if it's lower priority stuff I will say "I don't know, I wasn't listening." Her usual reply is "then why do you have all of them on?" When I try to explain I only listen to the big stuff she shakes her head.
The secret of course is that we train our minds to only listen for certain words, phrases, as well as the tone and rhythm of voices. Everything else just passes through the filters without stopping. It is just one form of multi-tasking. Parents with small children can tune out the sounds of everyone else's child in a room while just focusing in on their own, and can tell by smell if it is their baby whose diapers need changing. They tune out certain speech and sounds their children make at home but go running for others. The mind is amazing!
Browning, another thing that happens when you are in the hobby long enough is that you buy radios as significant new features are added to them. Quite often you don't get rid of the old ones and find good uses for them. I have a PRO-2006 that does not have trunking capability, CTCSS tone squelching, or alphanumerics. I now use it to listen to one system where those features are not needed. I have a PRO-2052 that I use to monitor certain talkgroups on the trunked system of the local major ski area. It does not have alphanumeric capability either. I use it to listen to about four talkgroups that have the most important traffic on them (weather, snow, and road conditions). With only four I've easily memorized the talkgroup number and associate it with a channel on the 42 channel setup that ski area has. If I am listening to their entire system I find it impossible to recall the use of each talkgroup by number so I use the BC-780 with alphanumerics in that case. I have a two meter ham radio as well as an HF to 440 MHz base station. If I'm working another band, I like to have the two-meter-only rig on to listen for local traffic or another repeater. I've only gotten rid of radios that don't work and can't be fixed. All the other radios I've obtained over the last 40 years in this hobby I still have. Many of them are located right next to the desk in my home office/radio shack. Sometimes when I'm mobile I want to have more than one handheld on search when I'm figuring out a radio system or trying to find what frequencies are in use, especially when looking for business frequencies being used without an FCC license.
At some point, depending on the circumstances, you begin to shut off radios so you can focus entirely one one incident, or the communications of one portion of an incident as you find that every word is important and you can't miss even one. Otherwise you begin to lose track of what is going on. This changes at different stages of an incident, which finds you turning up or on some radios, then turning down or off other radios several times during the course of the incident. Then the phone rings or your wife tells you there is a funny noise in the washing machine and you miss the most important words in spite of all your dial turning efforts!
The bottom line is that anyone that stays in a hobby long enough appears to be pretty weird to newcomers and people not familiar with a hobby. How many times have you heard "man, he/she is really into it and it's pretty weird!"