On at least some runway crossings, the pilot can’t look back to the approach area. It’s too far back over their shoulder to see. For the more typical case where the taxiway crosses the runway at 90 degrees, the approach area is visible if someone both looks and sees. Pointing your face and eyes out the window is not the same as seeing; that requires a conscious effort to process the scene & focus at the appropriate distance(s).
As to “supposed” …
The actual aviation regulations with the force of law address very little of pilot operating practice.
There are separate “best practices” books put out by the national regulator that contain a lot of the actual details on how to aviate within the system correctly. All of which have some force less than law, but more than mere suggestion. Sorta like “do it this way unless you have a darn good reason not to”.
For a hobbyist pilot that’s all there is in terms of mandatory & semi-mandatory guidance.
For an airline or a quasi-airline like NetJets of FlexJets, they have an official pilot procedures manual which can go into painful detail with a script for nearly every activity. Or can be more cursory. In any case, this document is blessed by the regulating agency. At which point it becomes a legally binding mandatory thing with the force of law for the crews of that company.
For smaller bizjet operators, be they charter operators or just a corporate flight department with a couple jets & a few pilots, they may or may not have any such procedure manuals. But if they do, they’re a) likely to be pretty cursory, and b) do not carry the force of law.
General best practices are for both pilots to stop doing anything else while the airplane is pointed towards a runway. Approaching the runway both pilots say something standardized to indicate they see the thing we’re approaching is a runway, we both intend to cross it, and we both have clearance to do so. Then we turn on a bunch of extra lights, look both ways, and tell the other pilot we have done so and see nothing concerning. Then we enter the runway.
That’s how I did it for 30 years at 2 major carriers. I can’t say the policies are just like that every quality operator, but they probably are close.
Back to this instant case, with all the flubbery on the radio it is unclear to me that the crew understood they were supposed to hold short. Midway is also rather a lot of confusion stuffed into a fairly small space. Lotta ways to think the runway is the next perpendicular pavement ahead of you when in fact you’re already on it. Oops.
It’s also smelling a bit like too much hurry and not enough deliberateness. Which I am told is a bit of a problem in a lot of the bizjet world, even the big operators.
