Ham
The 'scan' that you refer to is called the 'instrument crosscheck'.
For starters, the crosscheck is not a random look across the instrument panel. It is a specific process that begins with the understanding that there are two types of instruments...control and performance.
The basic idea is that the pilot uses the control instruments to establish a desired aircraft attitude. Then, he uses the performance instruments to check whether or not that attitude does what he wants (for example, hold level flight or a desired airspeed).
There are two control instruments...the attitude indicator (ADI) and the engine performance instrument (usually a RPM gauge).
The performance instruments are all the rest...airspeed, altitude, heading, navigation, climb rate, etc.
The process is for the pilot to set a pitch and bank attitude on the ADI and a power setting on the RPM gauge. Then he checks his airspeed, altitude, etc to see if the chosen attitude and power setting are getting the desired result. If not, he goes back to the ADI and RPM gauge and makes a correction...and then repeats the check of the performance gauges....over and over again!
The instrument crosscheck always starts with the control instrument, goes to a performance instrument, and then returns to the control instrument. That is why the ADI is centrally located in most instrument panels and HUDs. The ADI is like the hub of a wheel and the spokes go out to the performance gauges.
The important point to remember about the instrument crosscheck is that there is not just one. There is a specific crosscheck for each maneuver. For example, if you were making a level turn to a specific heading, you would be crosschecking attitude against altitude and RPM against airspeed. Heading would not be important until you approached the desired roll out heading. The nav instruments would not be in the check at all. If you were doing a climb at a constant speed, the performance instruments that you would be concentrating on would be the airspeed and heading. For an ILS, the workload would increase significantly because more of the performance instruments become primary...airspeed, descent rate, heading, glide slope, and course.
Our sims make an excellent instrument trainer. In fact, I think the typical sim is more difficult to fly 'on the gauges' than a real airplane...the reason is the imprecision of our control sticks and throttles.
Hope this is what you are looking for.
Andy