Man, I see a lot of frayed cable ends! I guess the finishing touches have been lost over time.
I had a neighbor kid come over the other day and asked if I could fix his brakes on his new bike. The cables were so frayed, they looked like an old toothbrush. "Did your pappy do some work on the brakes?" I asked. "No, we brought it back to K-mart where we bought it and asked them to fix it, but the brakes still don't work" he said.
Look, most of us don't have the big box of 400 cable end blunts and most of us don't have the skill to solder the cable ends either. Tape wrapping is promising, but doesn't work well.
Here is a simple solution : finish the raw cable ends with a lead fishing sinker. Just open it up, slip the cable end inside the sinker, and mash it flat with a pliers. Done - professional, beautiful, and lasting.
If you are a perfectionist, use a torch to semi melt the sinker to a droplet shape.