@LAB27: Yes that’s the photo I was thinking of, well found!
@RRK: It’s an exceptionally good question which Medved has already answered very well. I can only add a little more.
What determines the quantity of halide in the arc is not its boiling point but its vapour pressure. Even some solids produce vapours (think of solids we can smell). The starting point for metal halide lamp design is an atlas (produced by Venture’s subsidiary APL with additions in dozens more scientific papers) of how the vapour pressures of the salts of interest change vs temperature and physical pressure. Since the 1980s-90s that has become pretty well known for each of the individual halides.
When we then prepare binary mixtures, the vapour pressure of one component is influenced by the other. Exactly the same principles apply as in alloying of metals, in which the melting point of the alloy is typically lower than either of its components, and changes with composition. A 2D phase diagram then has to be made to illustrate how MP changes vs composition. The same can be made for vapour pressure. Ternary and quaternary mixtures are the norm in most metal halide lamps so we need 3D and 4D phase diagrams - and hundreds of metal halide lamp engineers around the world have served almost their entire careers on that line of research. Since the 1980s it has been done by computer models built by each of the lamp companies but usually always shared between each other. The results can then be plugged into the lamp design modelling software which is usually more confidential.
Conclusion : adding more of one component to a big salt pool in a lamp can still change the vapour pressure because it changes the chemical composition of the melt, and the weak intermolecular forces that govern vapour pressures.
A second explanation is that the temperature gradients in metal halide lamps are often extremely sharp. At the cold spot where the halides reside, gradients well over a 100K/mm are not unusual. So increasing the volume of salt changes its temperature and vapour pressure. Additionally if you look at a burning metal halide arc tube (best by using a projection lens to image it on a screen) you see that the halide is not usually restricted to a well-defined pool with sharp edges. Due to surface tension and energy influences with quartz/PCA a kind of mist-like deposit may creep as much as half way up the wall. The distance is influenced by the total quantity of salt and since such areas are very hot (but only contain a tiny amount of halide) this also contributes to the quantity of vapour entering the plasma.
Moreover a bigger pool also absorbs more radiation from the arc and is further heated beyond what might be the coldest temperature at an infinitely small spot.
Probably there are other parameters as well but since I did not work so much in that area I only became aware of the general principles. I will definitely ask some of my remaining lamp chemistry colleagues at work for further experience!