Step 4: Fake welding
1. Get two (or more) pieces of wire lined up
2. Prepare some JB Weld
3. When it is somewhat hardened, coat the joint in the mixture
4. Wrap the joint in the silver ribbon as smoothly as possible, and tie off the end.
The tips (not pictured here) are the hardest, since you have to get several points together at once. I believe I did one connection at a time. Wrap two wires together, then the two with the next one, and so on Bulkier connection, but less likely to fall apart.
This picture shows a close up of a several connections from later in the project.