To show TIG filler wire feeding there are two movies provided.
They show two / three stages
With the steady forward-feed, feed the weld pool with the wire on the forward feed of the wire with the fingers. That keeps the hand always the same distance from the weld pool. Can train hand so that on the re-grip, gripping wire with thumb and retracting fingers fast regrip, can move hand forward to maintain feed then return hand to chosen stand-off by feeding faster through fingers than into weld pool for a moment. So can keep an absolutely constant wire feed.
In this video, the end of the wire is waggling. For welding, one would have to keep the forward end of the wire steady.
Can superimpose a slight dipping motion in and out of the weld pool which is normal with TIG (geometrically, that's a rotational movement transverse to wire feed direction).
I haven't TIG welded for two years. However, I made stainless objects to sell at craft markets for a while, and practiced this action for hours on the train home from work - had my TIG gloves and 1.5m of 0.8mm TIG wire in my briefcase.
When exercising this, the wire is always gripped. Either the fingers are gripping or the thumb is gripping. At no time can the wire "slide". Someone pulling or pushing on the wire can neither push it forward nor pull it backwards in any ways apart from what your feed motion is imposing. You can grip the wire yourself and force your fingers to exercise to a higher strength, so the feed when welding is within the "easy" range for them.
Here is a close-up with gloves off of what the action is. I've always used the yellow "TIG gloves" when TIG welding.
For the first three images of the "forward" feeding motion, the thumb is a soft guide upon the wire. For the fourth "return" picture, the thumb tightly squeezes and clamps the wire.
Beginning of forward feed motion with fingers
Middle of forward feeding action
End of forward feed with fingers extended
The "return" sweep of the fingers (exaggerated finger release from wire - in reality you would slide the fingers back along the wire). Thumb gripping wire.
TIG welding with gloves - often you see pictures of people TIG welding without gloves. These yellow gloves are "TIG gloves", of thin stretchable leather. The other manual electric welding processes (SMA and MIG) need the use of heavy hide gauntlets. It was recently commented on the sci.engr.joining.welding newsgroup that if you do TIG weld without gloves on, your hands acquire an odd smell, which is due to the ultra-violet radiation breaking up the proteins in the skin.