how do you gauge and judge "timing"?

Hmmm, haven't heard that one before. 

If you want to understand the terminology of high end audio. I recommend The Complete Guide to High End Audio by Robert Harley. It is the reference guide to high end audio. 

The way I judge is by listening to songs I know well and then decide if the system sound "right" 

Obviously lots of room here for interpretation however over time if you remain aware of these attributes you will become better at gauging, 

PRat, Pace Rhythm and Timing.

Heavily promoted by Naim Audio, gets your foot tapping.

Loved or hated, sacrifices detail.  

Ahhh, yes... embedded in PRaT (I usually refer to it as Rhythm and Pace). I must admit when I sense PRaT, no part of that feels like timing to me. But, your right, there is it is.

Just as a comment on PRaT. It is probably one of the most important characteristics there is in music. It is what involves you emotionally and makes you tap your foot an sway. It is also one of the most difficult to sense and identify. This is because it isn’t a specific locatable sound quality. You can’t really point to a place in space at a sound and say, hear that... that is PRaT. It is a gestalt characteristic. It took me over thirty five years before I was able to identify it. Like a lot of parameters in music, once you hear it... then you can identify it consistent. 

When I think back in time, I can remember systems that had incredible PRaT... an how they impressed me... but couldn’t tell you why. Often the ones that displayed it the most were emotionally captivating but really lacked detail. When the balance is right with detail and PRaT... to my mind you have a really audiophile system... The thing that reproduces the whole experience. 

Anyway, don’t expect to just sit down and hear it. It often takes years to recognize it. I have sat with experienced audiophiles and helped coach them to hear it. 

One of the scenarios that have often had a huge amount of PRaT (live and in recordings) is really good drumming groups... typically African or South Pacific. all sorts of different drums simultaneous in perfect rhythm... hmm somewhere in there must be the timing thing.. 

time alignment of speaker’s drivers is an issue (not the speed of sound) the physical alignment of the drivers to each other, see the diagram

https://en.wikipedia.org/wiki/Loudspeaker_time_alignment

here, JSE (many others) slanted the face of their Model 2 Speakers

Here, I tilt my speakers back, it’s to aim the tweeter’s up for both time alignment and directivity of the tweeter to seated ear height

I put a 2x4 flat above the front wheels to tilt them back