OK, so after 7 years it still is not understood. Here is the chemist's POV and explanation:
Borax, as in 20 mule team, is any of several related compounds of the element boron.
It is mainly sodium tetra-borate.
It is hydrated with water that is tied to the compound by being bonded in the crystal structure. The usual hydration is decahydrate.Ten water molecules bonded to the sodium borate molecule. Na2,B4,O7 (10/H2O) [Actually it is a bit more complex than that, but this will do for here].
Now, when water is bonded to a compound, it won't just dry up. The bond needs to be broken. The normal way to do it is with heat. If just a little heat would work, you could just set the borax box out in the sun and it would miraculously convert into anhydrous borax. However, these bonds are a bit tougher than that. If you left it out to dry in the sun, it would ,over time,loose only about half of its water. It would degrade into tincalconite, which is sodium borate with only five water molecules bonded. Still a long way from anhydrous.
To make it anhydrous, you have to destroy the water bonds, fuse to sodium borate into an amalgous mass, and drive off the water ( the easy part). Then you have to grind the anhydrous borax back into a powder to make it useful ( not the easy part). Storage of the anhydrous material must be air tight, as it is hygroscopic, and will slowly degrade back into hydrated borax.
Purchasing anhydrous borax in sealed containers and keeping it sealed is the simplest way to deal with this. Baking it in the oven yields tincalconite and a mix of hydrated borax compounds.
HOWEVER, all that is only if you NEED anhydrous borax. While it is nice to use as flux, it isn't necessary.
First, lets discuss flux. The welding flux you purchase is a mix of borax ( usually partially dehydrated), ammonium chloride, and boric acid. Many other things are added to the mix depending on the usage, and the proprietary formulation of the seller. These include fluorspar, powdered charcoal , iron filings, and several other reducing agents.....even fine sand.
The main ingredient is the borax.
In welding , the billet/bar is brought first up to around 1000F, then pre-fluxed. This allows the borax to stick to the hot steel by dehydrating the surface of the borax particles as they hit the steel. The steel is returned to the forge/oven/furnace and heated toward welding temperature. On the way the borax dehydrates easily, gassing off the water vapor ( the bubbling stage), and coating the steel first with a crystalline coating of borax, and then with a molten coating of anhydrous borax at 1400F ( the hot honey stage). More borax is usually added somewhere near the welding point to assure the surface is completely de-oxidized. This coating (along with the other fluxing agents) causes the iron oxides and other surface contaminates to have a lower melting point, and thus "cleans" the surface to prepare it for the weld. As the steel approaches the welding temperature, the borax starts to eat into the steel ( 2000+F borax is extremely corrosive). It allows the iron filings (if present in the flux mix) to melt and fuse with the steel, and causes the steel to bond together more easily. When pressure is applied to the steel pieces being welded ( hammer/press/flywheel/drop forge/etc.) ,two things happen almost simultaneously. First, the very fluid flux is expelled from the joint ( assuming the joint was properly set up, and the pressure is properly applied) ,carrying the dissolved oxides and contaminants away with it. Next, in this now pristine environment, the atoms from one piece of steel bond to the atoms in the other piece by having the grains grow together. This makes the weld joint clean and homogeneous ( in a perfect world) or at least fairly clean and very strong ( in our world).
SO, you don't need to use anhydrous borax, since the plain hydrated stuff automatically converts to it during the fluxing process in welding.
The mix I use is 25% boric acid and 75% anhydrous borax. This is because I have a 100# barrel of borax, and a 50# barrel of boric acid. I also realize that the 30+ year old stuff is not chemical grade anymore and is partially hydrated by now. If I was to need a new batch, I would buy plain borax.
A final note about all that hot, molten borax.....It drips all over the floor of the forge. As said, it is corrosive, and especially so to things like mineral wool and satanite. It will eat a hole in the floor of the forge after a while. You can deal with this by periodically replacing the floor of the forge, by covering it with a replaceable refractory material ,like fire brick or kiln shelving, or using a flux resistant refractory coating like bubble alumina. Poured ( rammed) refractory is also fairly flux resistant.
Stacy