Is sundial time entirely dependent on solar azimuth? I've visited several "how sundials work" sites and can't seem to get a 
clear answer to this: is "sundial time" just a linear function of 
solar azimuth? More specifically: 


When the sun is due south (northern hemisphere), it is sundial 
noon. All sites I've visited agree on this. 
When the sun is due west (azimuth 270 degrees), I say the sundial 
time is 6pm, a quarter turn/day from noon. However, I can't find a 
site that actually says this, and some sites seem to disagree with 
this. Same for it being 6am sundial time when the sun is due east. 


I know there are different types of sundials, but had always assumed 
they would give the same sundial time. Is that not true? 

As a note, the sundial I describe above can be fairly inaccurate at 
times, which makes me question whether I'm correct.

EDIT (to clarify question): Forgetting entirely about clock time for a 
moment, suppose I build a sundial. When the sun is due west, my 
sundial reads 6pm. When the sun is due east, my sundial reads 
6am. When the sun is due south, my sundial reads noon. My question: 
have I built my sundial correctly? The type of answer I'm hoping to 
get: 


No. When you build a sundial, it should read (something else) when 
the sun is due west. 
There are many different types of sundials. Depending on type, 
your sundial may or may not read 6pm when the sun is due west. 
It depends on your latitude: sundials are 
latitude-specific. There's no such thing as a global sundial. 
Yes, your understanding of a sundial is correct. Sundials can be 
off by as much as (some number/formula) from mean solar time, 
depending on your latitude. They can be as much as (some 
number/formula) from clock time, depending on your longitude and 
time zone.
The sundial translates the position of the sun to the time of day, so it depends on the path the sun takes across the sky, this is called the ecliptic.

Because the earth's rotation is tilted with respect to its orbit around the sun, the ecliptic shifts across the sky during the year, which is also the cause of seasonal change on earth. Yet the highest altitude of the ecliptic will always be due south, which means noon is well defined every day of the year.

Now to answer the question; if the day length (from sun-rise to sun-down) is exactly 12 hours,  the sun will rise at an azimuth of 90 degrees and set at 270 degrees. However, this happens only twice a year, namely at the vernal equinox (first day of spring) and the autumnal equinox (first day of fall). 

At the longest day, the summer solstice, both sun-rise and sun-down azimuths will be at their highest shift northward. On the other hand, during the shortest day, the winter solstice, the azimuth-shift will be maximally southward. This last bit applies to the northern hemisphere, for the southern hemisphere the seasons and therefore day lengths are reversed.  

So in short, you have to account for what place on earth your sundial is at and what time of year it is.