I want to thank everyone for your kind replies. I have done a few tests and wanted to report back. Hopefully this can be a help to others, as before I did this I had made a grand total of zero of these. These results are what happened to me and the failures are not to say that they don't work. They just did not for me.
Some things that I found:
Stretched plastic Q-Tips did not work for me. I could not get the stretch long enough to get the tube thin enough. I was shooting for the .5mm brass tube that I had on-hand. After about 30 minutes and a couple dozen tries, I shelved that one.
Razor saw was too bulky for me and the size seemd to overwhelm the tube. I shelved that one.
I tried cutting the tube with very sharp scissors, various "snips" and always ended up with a crushed end of the tube. Shelved those methods.
Found the small K&S pipe cutter at the LHS and grabbed it. Should have read the label. The smallest diameter it says is 1/16". I am using .5mm or slightly larger than 1/64. Shelved that tool.
So, what did finally work? The winner is:
I laid the flat tube on my cutting mat, and found the length I wanted. I placed a breand new number 11 blade scalpel on that spot and rolled it over the tube going back and forth about 4 to 6 times with medium pressure. Think of those loggers rolling a large log with their feet while it is floating in the water. I then checked and could see a visible "scoring" of the tube. I then put the tube into a small set of soft nose pliers just about to the score line. I then lightly moved the other end of the tube back and forth and it snapped in half. I inspected and thought I had a pretty clean break with no crushing. Now on to the eyelet.
This was much easier. I used 36 gauge annealed wire from TEMCo. Item number RW0189. I cut a piece off with sharp scissors about 3 inches long. The length is not really relevant, I just wanted a long enough piece so I could handle it. I folded the wire into what looked like a tennis raquet frame. I then took some large hemostats and clamped off the handle end of the raquet. The large loop end was then placed over a .3mm diameter drill bit that I had placed in my hobby drill. Keeping slight pressure so as to not bend the drill bit, I twisted the wire until I had a twist with a very small loop just slightly larger than the diameter of the bit. For those of you who have done it, think of safety wiring a filter or other thing to an engine. I then slipped off the wire from the bit and released the hemostat. The end clamped was then cut shorter with the scissors to make a sharp clean end. I then took that end and slid it through the tube like threading a needle with a thread. The long "extra" can then be CA glued and trimmed down as needed. By the time I was done, I was making one of these every couple of minutes.
Here is a picture of two that I made.
I am sure my scale is all out of proportion, but I was thrilled to be able to make it happen. I loved the look of those that are available to buy, but two bags of those and it would be more than the price of the kit.
If anyone wants more info, just let me know. Thanks again to everyone for your help in explaining your techniques!