Google gives us 528 page .pdf named Phase Transformations in Metals and Alloys (2. ed. 1992). I can´t take that much science even if it was in Finnish. It does not contain words etch or acid, but maybe it holds the secret.
Ragnar,since i was the one who brought in the weird terms,i'll try to put it simply:
When we choose to harden steel we Thermo-cycle it in a given way.
In the process of heating and cooling steel undergoes changes,going through so-called Phases,which in turn affect the micro-structure of steel.
With Carbon steel the common desired state is called Martensite,it's a Phase that allowed the steel to accommodate more Carbon atoms inside the structure,making it denser(we call this Hardness).
Martensite is arrested by rapid cooling(quench)and so the changes to the micro-structure remain permanent.
Science is actually kinda undecided if Martensite is a Phase,a structure,or both,and so i was wrong to use the term Phase Transformation.Phases Cause the changes to the micro-structure,and that's what we're interested in.
So,the "temper-line" would exist if indeed we could see the difference in micro-structures,between differentially heat-treated portions of an axe.
Could do so with a naked eye,maybe with the help of an etch,et c.
Indeed,such thing can be.Under very high degree of polish we Can indeed see some things there.Under Uber High polish,like in the Japanese tradition,going into tens of thousands of grit,things get real interesting

But,none of them look like an axe blade(generally, hardened areaslook lighter in color and of course glossier,being denser taking higher gloss).
And,we're talking wire-brush finish on surface...AND,very mildly acidic etches...(knifemakers labor at it with things like Nitric and other intense acids).
So,a number of things do not quite compute.
But they instantly fall into place if there's a joint between two dissimilar alloys.
Presence of Carbon in alloy responds to etching immediately and very starkly.And since it's for that difference that we'd likely use that method,to have a hardenable edge...
But metallurgy is a mystery still,and sometimes hardened steel Does etch dark...

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This is to quickly recap for you some previous discussions,sorry if it's longwinded...