Kirk,
Looking at that, too much flux and maybe a bit too much wire, but because it hasn't penetrated the joint, it might be the correct quantity.
Silver solder requires a gap of approx 0.002" to penetrate down to join the parts together.
With tubing make it a slight slack fit, and very gently flatten the end of the tube into a slight oval. This will make it tight in the hole, but allow the solder to penetrate.
Do the same with solid rod or whatever, but tap the rod with a hammer or centre pop to deform it slightly (only on the area inside the hole, so it will not be seen). Again this will hold the rod tight, but allow the gap.
I normally paint a tiny amount of liquid flux down the hole, and only on the very end of the rod or tube and assemble them all together. You should only see a tiny amount of flux on the surface.
Wrap the wire around the rod or tube like a spring, and cut along it's edge. This will give a series of rings that will easily slide down the tube or rod, flatten them straight before use, you should be able to do it with your fingers, locate it down against the hole. Just use one ring for normal, two rings for a deep hole.
Do not play heat directly onto the flux or solder, only onto the main part, in your case the big bit of brass, somewhere around the other hole, or the end of the metal hearest where you want the joint, and watch the heat travel towards the required joint. As it heats up, the flux and solder will melt and flow into the gap around the two parts. As soon as you see the nice fillet form, take the heat away, wait for a few seconds and then drop it into a quench tank or your pickle bath. Half an hour in the pickle should leave the job completely free of flux and maybe a bit of copper plating over the job, this should easily be polished off.
If the part gets to bright red heat, you've cooked it. Usually a dullish red is sufficient for the main component.
These instructions are for the special flux and wire I have sent to you, other fluxes and solders might react in a totally different way. Especially plain borax, it is not worth even trying, you will never get a perfect joint with it. OK for the 1950's, but not modern day materials and solders.
The main problem with silver soldering is usually too much heat, too much flux and too much solder. Use the minimum you can get away with. If it is not enough, you can always put another drop of flux and a ring of solder and reheat. Just always watch for when the solder flows.
Hope this helps, if not, maybe a change in technique for your style of soldering. You will get it eventually, and once you do, it should be with you for life.
John