I used to braid both ends, but the results weren’t great. The braid would tend to fray and then the connection would break.
I get much better results using 22 AWG copper with with silicone wrap. I bend the top end of the wire so it can hook over the top of the spring. The bottom wire goes below the spring or is tucked into the bottom-most coil. I then solder the wire on.
I typically do both head and tail springs the same way: with the wire inside the spring.
To prevent the solder at the top of the spring from wearing out and breaking off, I now always solder a small copper disk to the top of the spring on top of the wire. This greatly extends the lifespan of the bypass and lasts much longer than solder braid.
I have some 18 AWG wire but have never used it. It’s so thick, I don’t think I could get it inside the small EDC lights I tend to mod.
For drivers with a particularly small or hard to access contact pad, like the H17F, I use the same technique as above, but might install the spring inverted so it’s wider at the top. I still have a copper disk for where it touches the battery though.