Mustang is a high profile State Alchemist who served in the Ishval campaign. Scar has just resumed his killing spree. If Father decides that Mustang needs to go, he'll have Lust leave his half-disintegrated body on a street somewhere and let everyone jump to the most obvious conclusion.
I doubt Sin Inc will jump to that solution immediately, though. They want to preserve as many State Alchemists as possible for Father's sacrificial ritual, and they've already lost a good number thanks to Scar's actual attacks, so they'll be reluctant to waste another. So, I predict that they're going to make another attempt to stall or misdirect Mustang, and then resort to framing Scar for his death if that fails.
On a metafictional note, this also explains why Scar has continued occupying so much narrative focus. The pieces are coming together.
Also a problem with that is that Mustang's fighting style is very distinct and very very loud.
Dude won't go down quietly, and it's not anywhere near certain that Scar could off him before the fight has an audience of the entire city.
This is starting to feel like a systemic problem in shonen anime. JJBA also did this a bunch of times. It's like there's this weird paranoia about the audience not being invested enough to feel for the main characters' substance, and so it wildly overdoes the set dressing in the hopes that we'll be effected by a sufficiently large amount of style. It's pretty condescending, and it makes the storyteller come across like a con artist trying to razzle dazzle me away from some critical flaw that would ruin everything if I noticed it.
Its just the shonen aesthetic, keeping in mind the target audience is in theory tweens to teen boys, emotions are overwrought, everything has to be declared, possibly with big title cards.
Good point on Mustang's behavior here. That doesn't make it any less stupid, but it's a realistic kind of stupidity.
I think Gluttony's most important use for the group is his sense of smell. He was able to locate Scar by scent, without ever having met him before, across a densely inhabited major city. Removing murder evidence is fairly easy in a world where alchemical disintegration is a thing. That kind of tracking ability, much less so.
On a related note, it's a bit of a headscratcher that the haemonculus with the most publicly visible role is also one of the least capable of passing for human. I'd assume that Wrath was just the least bad option for the job since Envy and Lust were needed elsewhere, but it was stated that Wrath was PURPOSE BUILT for this role, so...what the hell was Hohenheim thinking?
What we've seen:
-Lust - 'low' power, other than the base homunculus template stuff and her Maximum Fingering Penetration, but has no severe psychological issues.
-Envy - Extremely versatile shapeshifting, would make an amazing infiltrator except they have no impulse control, and will break cover to get their jollies if triggered.
-Gluttony - Combat monster, he fights like a boss monster. But he's literally retarded, and has impulse control problems.
-Wrath - Very much human template, his special power is basically the Sharingan(at least before they put bells and whistles on), and he's visibly stable even in long term engagement with people.
-Greed - Adamantium Exoskeleton, but otherwise more or less standard human template. Is fairly sane and stable, able to philosophize and decide that no he's not going along with the plan. He's like the inverse of Lust really, his special power is a one trick super defense, just as Lust's is a one trick super attack.
-Sloth - ???
-Pride - ???
So we see that the more powerful ones are also the ones with stability/control issues, the ones closer to human template are the ones who are...well they aren't particularly exceptional people outside of being regenerating super strong monsters, but they also are fully human smart.
Also considering the gender balance of Amnestris' military, I suspect the main reason Lust isn't the Fuhrer is she has boobs. Envy would make a terrible Fuhrer, they enjoy themselves too much.
Okay but like.
Wrath actually takes to the battlefield in person sometimes, and he's the kind of dictator who'd naturally attract assassination attempts besides. Also, um...he has a habit of climbing through windows and shit out in public during the day.
It just seems like the eyepatch being cut/caught and coming off could very easily happen, and not necessarily at a time and place where he'd only have to kill one or two witnesses.
This IS the same guy who moves fast, strong and precisely enough to sever a weapon threatening him in the instant of its approach without the attacker realizing it until they moved and the weapon fell apart.
Somehow I doubt it'd be happening short of an artillery or alchemical assault, except the Fuhrer there is the guy with the armies of alchemists.