Theories about the inspirations of Scaramouche's multiple designs that seem believable to me. Might remove or add more stuff later (remove if it's proven false; don't wanna spread misinfo.) Just as a general note here: Scaramouche has clearly things in him that were inspired by Neon Genesis Evangelion, and the giant mech suit is no doubt one of them.
Kabukimono
Scaramouche's original outfit as Kabukimono. It's not particularly surprising that he, as a divine creation, has a religion inspired outfit: his general clothes (the white ones) resemble the traditional clothing of Shinto priests. It looks like Heian era men's clothing.
Around his neck, Kabukimono has the golden feather he got from Ei, the proof of his identity. It is tied with strings that resemble puppet strings (to me). His haircut resembles the hime cut (princess cut) at the sides. However, hime cuts tend to have short hair in the side and long hair in the back - Kabukimono has short hair in the back.
In some images, he is seen wearing a purple veil on his head, although he took it off sometimes (like then learning bladesmithing). It has been theorized that this could be a katsugi or kazuki veil, a veil that was worn by noble women from the Heian period onwards to hide their faces in public as well as protect from insects and dust. These veils later changed form, being attached to hats or even just a robe put on ones head so the collar obscures most of the face.
Scaramouche
As Scaramouche, The Balladeer his clothes have changed to dark colours. He has shorts and a short robe that resembles more of a later style kimono or hakama. He has many kabuki theater features on him, such as the white and purple rope and plum blossoms on his ornaments.
On his hat, he has ornaments that look like the paddles used for playing the shamisen, a traditional Japanese lute. On the top of the hat is a face that looks like kabuki makeup. Fun fact: Scaramouche of Italian theater didn't wear a mask, and neither does Scaramouche of the Fatui, unlike most of the other members. At the back of the hat, he has a veil, and indeed, it is as you have guessed. I foreshadowed before that in later periods women used veils attached to hats to cover themselves. Not that Scaramouche's veil does much to hide his face.
The ring of his chest resembled the electro symbol to me, but it is a circle with what looks like three birds. The same symbol is in the bag on his back.
Wanderer
Wanderer's outfit is full of references to Buddhism and shugenja monks, which is what he was called in the game itself as well. The ornament around his neck actually holds a sutra - a Buddhist text is rolled up in a cylinder for carrying. His signature weapon, Tulaytullah's Remembrance, looks like a ghanta bell, which is used for ritualistic practices in Hinduism.
In addition, Wanderer also has some bird imagery as there are flying birds in his robe. The birds also look a bit like leaves. His hat lacks the veil now, and actually resembles a monk's hat that is supposed to represent a halo (and it becomes one in his windfavoured state). Its shape looking from the top looks like a lotus flower. The ornaments looks like upside down shakujou staff. Of course now, the has the vision and where the feather is hanging - the vision is right above the spot where his heart should be.
Bonus
Some fans have pointed out that Wanderer's attacks reseble those of Ruin Guards and, well, he is a puppet built according to a Khaenri'ahn technique...
His skill and constelation names have a lot of references to theater and especially Japanese noh theater.
A lot of this information comes from Ashikai's video [3.3] The Complete Scaramouche Design Analysis. However, while watching these kinds of videos, it's always good to remain skeptical because these are, in the end, only theories. (The amount of times I've seen people repeat this video's Makoto theory as fact even though it's literally just speculation.)
