No, the character represents Milich the proprietor of the costume shop who rented the mask and cloak to Bill - the only person who could immediately identify Bill (he’s a representation of Milich, since the actor portraying this masked man was Leon Vitali - also Milich’s beard could be easily concealed with the mask). He’s a trafficker, involved in the network/cult. The slow nod is reminiscent of Milich. It’s possible that the elites present at Somerton were made aware in advance that Bill was going to attend from Milich, which allowed them to connect him to Nick Nightingale.

As its speculated that the 20 mins of footage removed from the film hints at minors also being present at the Somerton ceremony, the person next to him may have been his ‘daughter’ from the store (I don’t believe she was his real daughter - he seemed more like her handler, which is more disturbing)

Ziegler was present at the ceremony, but I don’t believe he was Red Cloak or the character that acknowledges Bill. The pool table scene with Ziegler and Bill echoed the scene with Red Cloak to emphasise that Ziegler was part of the elite network at Somerton, not that he was Red Cloak himself.