Quick question. is there an advantage to wrapping the string around the tail piece like shown in the picture? I never have done that but I see it often
No, you only do this if the angle from the tailpiece is so steep that the strings would lay on the corner of the bridge (i.e. very steep angle). Other have mentioned the string-breakage that probably is related to the steep angle. On some set-neck guitars the neck angle is glued in so badly that you will run into problems otherwise. I've seen an SG once where you had to either leave the tailpiece superhigh or the strings would lie on the edge of bridge, and a luthier once claimed to me that Gibsons' neck angles can vary quite a bit (because work staff have to get through many guitars quickly on a day) and then they are far from the "perfect angle" you'd have if you went to a smaller company. I have no way of knowing if that is true or not, but I once saw a factory tour video from Gibson where the guy fitted the neck tendon in the body in quite a "rough and rustic way" with a hand wood chisel, without any measurement.
It may simply not be a big deal, given that both bridge and tailpiece are adjustable on Gibsons and thus able to deal with the variance.
Putting the strings the other way around the tailpiece helps with that. I have no doubt this is where this practice comes from and THEN somebody started "bullshiteeting" people that it sounds better (just like EVH made up all the Variac bullshitee, or people started saying the original Rectifiers sounded better when they never did). There are no tonal changes whether the string goes over the top or not, and it doesn't change the feel either. I've tried both versions and with different guitars.
The only thing that might be debatable is whether screwing the tailpiece all the way in, or leaving it a bit out, makes a difference in resonance. I actually think guitars vibrate a bit more when it is a bit out and not all the way down, but it's more a feel thing than a tonal difference.
