Gingor's page

Depends on chained monk vs unchained monk (or whichever of these an archetype is based on).

Monk flurry of blows is explicitly "like two-weapon fighting," so serpent runner could apply to the non-bonus attacks.

For unchained monk, two-weapon fighting is not referenced in flurry of blows, so the trait would definitely not apply.

I was specifically looking at the brawler(constructed pugilist) and the jistkan artificer magus, I should have mentioned that

So flurry of blows allows you to make all of your twf attacks with one weapon, serpent runner decreases the twf penalty for your primary weapon by 1. Would this allow you to lower the penalty on all twf attacks by 1 if you use the same weapon/only unarmed strikes? If not how would it work?