I have been told that for green western snaffle horses you should be holding the reins under your pinkies, not between them and your ring finger, which is prep for a double bridle your horse will never wear.
This person trains in a mecate -- those hairy round reins would be difficult between two fingers -- might influence this.
And of course, plenty of slack, this is one of those 'no, no, not continuous contact!' trainers. Actually very good for my trail horse trainee, as I sure won't be riding on contact over variable terrain and many miles.
When you ride western with two reins, as with a snaffle, you ride with a bridge
You also ride in such a way that the horse eventually learns self carriage on a loose rein, off of seat and legs
That means, you use contact, in training, as needed, while driving with legs, until the horse softens and then you release, expecting the horse to stay the same on his own (topline, speed and collection). At firsts you might only get a stride or so, before you have to take hold and drive, but you build on this, until the horse eventually stays correct without reins support
Even jr horses in a snaffle or bosal,a re shown on a loose rein, as they are not ready to be shown before then
If you always hang on to a horse, he never learns this
Far as mechanical hackamores, since they are not legal in judged events, it is pretty much 'anything goes, far as correctness
There are no 'pinky rules, riding with two hands.
Here is a video on using that bridge on a snaffle https://www.youtube.com/watch?v=Ky6KllDPGSw