Glass was chosen for several reasons - to give the electrode some rigidity, to keep the solder joint clean, to minimize the length of silver wire needed, to have something that you can insert into the solution that will not contaminate it, it's easy to clean, and can be supported in the solution using a ring stand clamp.
I think PE recommended around 2 cm of silver wire in the solution and I wanted all the wire under the liquid level so there's no possible changes as the solution level rises, so I wanted something that I could insert into the solution so I immediately thought of glass tubing. Commercial electrodes used to use glass, but now they often use epoxy for the electrode bodies. That was where I figured that 5-minute epoxy would be great for sealing the silver wire into the glass tubing. And it's much easier to use the epoxy and I think more water-tight than trying to seal the silver wire by blowing the glass to make a glass seal.
I wanted a technique that people without much glass-blowing skills could use. As it is, you'll need to practice cutting the glass, or get someone at a glass shop to do it. After cutting it, you'll probably want to fire polish the ends - Watch some online youtubes for basic glass-blowing techniques. None of this glass working is difficult and all you need is a glass triangle file to make a nick in the glass to "cut" it, and then a propane torch that you may have around the house already.
Oh, and when you connect the coax, just solder the signal wire of the coax and not the braided outer wire to the silver. Strip the braided part back a bit to it doesn't make contact with the center wire. It's going to take a fairly large piece of glass tubing to get the coax into the glass. Like 12 or 14 mm or so diameter tubing. Those are a bit hard to cut, so maybe a glass shop would be good if you've no experience cutting glass tubing.
I was also going to try making one out of acrylic tubing as it can be cut with a hacksaw - I bought the tubing but I never got around to making the electrode. You might want to git that a try. Other than the siver wire/rod, nothing it really expensive here.
And the coax I used was from Radio Shack - just a 2 ft coax with BNC connectors on both ends. Clip on BNC off and then you have a nice 2 ft lead on your electrode.