I wonder if the extra strap you see is where the Pisador {lead} attaches to the jaquima?
I know my friend when she bought her Paso tried him at the place there was what looked like a lead shank attached to her bridle...think that was where it was but not positive.
The true name for the Paso bridle part is "the jaquima" and it is similar but also very different than bitless or hackamore riding tack.
I found you a website that might offer a bit more information about the different types of actual nosebands, the fact that each is as individual a matched need to the animal as is any bit...and bits are also spoken of but most people do not need to ride in high spade mouthpieces as our own abilities and that of the animal are not so fine-tuned.
I also found you a visual guide of legal and illegal tack used, shoes and assorted equipment used on Paso horses...
Thought maybe seeing some of the pictures would help you in your choices of what to purchase or not as some things can be downright cruel and not appear it, hence offering a visual display for you to see.
As with any breed of animal...personality and pep in your step is a individual thing.
I've had the pleasure of riding a Paso that was as laid back and quiet to ride as any old nag, but a little leg and ask and a firecracker erupted of go, go, go...
I've also ridden Paso with that "brio" and honestly, it was exhausting to me to sit on a keg of dynamite when all was wanted was a soft, quiet hack to have this go, go, go under me pounding the ground as fast as the feet could go..
The breed though is taught to be fast in movements, the faster and flashier the better and some trainers punish if not enough "brio" is shown constantly.
In any case...
No expert on the tack, but saw many bridles at that barn we had gone to...
Along with the noseband thing was a separate bit hanger and then saw all the horses had a lead rope also hang from their bridle, thought it was from that "loop" on the noseband.
We do have some members with Paso horses who might be able to offer what is the use...
@knightrider comes to mind as know she has Paso so called her here to offer more insight.
🐴...
I personally don't own a Paso; I was just interested in that style of bridle. I appreciate you taking the time though! And I'll definitely take a look at that link.