One of the interesting things about the Wolfwood and Ninelives fight in Japanese that was a bit garbled or somewhat omitted in English, is that the entire thing is basically an act. Or at least is framed as one in a way that hints at Wolfwood's double agent status.
Like they are genuinely trying to kill each other to some degree because they don't give a singular shit about each other, but in the beginning Legato says "if he wants to show his fangs, it'll come at a high cost" and then he thinks to himself "He really is the right man for the job/well suited to his role, isn't he?" and while this is interpreted in the translations as him talking about Ninelives, he is most likely talking about Wolfwood there. In this scenario Wolfwood is playing a "traitor", which is funny because he IS supposed to be a traitor, but he's actually meant to betray Vash, not the GHGs. Nightow does a great job balancing the way the characters talk in order to hint at but not completely give away Wolfwood's true motivations/role quite yet. Even when telling Ninelives to deal with Wolfwood, Legato says that he'll rely on Ninelives to "handle" him, with some load bearing quotation marks included. And then at the end when delivering what he thinks is a finishing blow, Wolfwood literally yells "the curtains are closing on you, you lousy/ham actor" at Ninelives. Because Ninelives really hams up their anger in the beginning even though they likely wouldn't really give a shit about whether Wolfwood was actually a traitor or not (though they do seem to be angry for real in general which grows throughout the fight because of Wolfwood beating the shit out of them until they just kinda dissolve into yelling incoherently. Wolfwood actually tells them to stop being so cranky at one point because it's part of the job/business lmao). Partway through Wolfwood even comments on how he's a troublemaker who's always up no good, and that's what got him into this terrible situation (literally "this stinky/rotten place/position"), but even though he's sick of it, it's a hell he can't escape from (this part of his monologue is almost completely lost in translation unfortunately). Like that moment has a real "ain't I a stinker? That's why I'm doomed by the narrative" vibe lmao.
There are sooo many references to the overarching themes between both Leonof and Vash's fight and Wolfwood and Ninelives' presented through the framework of plays and theatre, Leonof tells Vash not to look away from the show when Vash is distracted by the explosion from Wolfwood's rocket, and after Vash shoots a real person unintentionally because he got too comfortable shooting the puppets, Leonof comments on how he has to keep things unpredictable (use an uneven/irregular tempo) in order to draw the audience in. Wolfwood calls Ninelives' abilities a ridiculous country act, and calls his acting terrible while saying the curtains are closing on him. Vash references Guignol, the famous French puppet from the old fashioned French puppet theatre shows that are named after him (the ones with the little hand puppet guys in the little wooden booths) etc.
Beyond just the puppet theming on a surface level I think these constant references to theatre not just with Leonof but also with Wolfwood is because Volume 3 is largely themed around hidden depths and putting on an act. There are the depths of emotions hidden under a surface that obscures it (Vash's calm/gentle expressions hide a dark abyss, Leonof's locked away memories hide the cause of the grief that drove him insane, Wolfwood's brash cynicism hides how trapped and hopeless he feels and his desire to be able to change), getting too lost in a role (Vash playing the gentle pacifist all the time and how unbearable that must be to maintain sometimes in the face of the terrible cruelty he experiences so often, and how inhuman that level of self control can make him seem to others, Ninelives eating the scenery, Wolfwood getting really aggressive from the start in his role of guard dog which results in him being stuck in a death match with Ninelives when they might have let him sit back and play defense without risking his own life as much otherwise), running from how you really feel (Vash's anger and sadness that he keeps a tight lock on, Leonof's grief leading him to seal his own memories away and do terrible things to learn to recreate real people as life-like dolls, Wolfwood's desire to be a better person and wipe his hands clean in some way which he pushes deep down because he doesn't think it's possible to break free from the chains of his past or escape from the hell he's stuck in), even assigning roles to others while denying who they really are (Wolfwood and Leonof dehumanizing Vash, Wolfwood being forced to play the traitor against his will in multiple different ways), or seeing past the mask to the real person underneath (Vash knowing who Leonof really is, understanding why he's made the choices he has, trying to reach out to him, Wolfwood realizing that Vash's inhumanity doesn't actually make him any less human than anyone else in all the ways that matter, the general theme through the series of Wolfwood and Vash seeing through each other's facades from the beginning and coming to an even deeper understanding as they get to know each other), etc.
I didn't really have a specific conclusion in mind with this post just had a lot of thoughts on the themes and stuff while reading Volume 3 in Japanese that I wanted to blab about lol.