Is Gauge the main thing?

Yes, of course, Gauge is an objective measurable factor in a string. Easy measurable. And it is the thing early music brands use to label a string, so it is universally accepted as THE thing we should matter of.

Gut can stretch more or less, depending on the quantity of twisting received, and on the chemical treatments made to have it stiffer. So we can guess something looking at the string, trying to tip the end on our fingertip to feel the stiffness, but we will not have a precise mathematical coefficient for our calculation of the correct gauge unless we make experiments and we are keen in math as engineers are.

That's why a gauge is a consistent trustable factor to reorder our strings only if we stick to the same manufacturer. If we change manufacturer, we will probably have to adapt our gauges to his kind of string.

Moreover, the gauge has no value at all when we speak of wound strings. Not only we cannot see and value the gut core features, if there is a silk cushion between core and wire, but we cannot know, by simply measuring the external gauge, the gauge of the metal, the ratio between metal and core, which is the main component of a wound string.

This is why when we order or reorder a wound string, the gauge is not something useful to the string maker to understand what is it.

And this, in the end, is why we need to test empirically our set of strings when we change brand or order a different string. 

This is the official pro technique.

The one I use for my strings is slightly different: instead of the pencil I use my teeth to keep the loop open, more practical.