Method 1:
If they are under vote pressure and are forced to claim, should they mention bulletproof or commuter, you will know the method required to kill them straight out. If they mention they have a resistance of some kind and don't specify, then you know it's one or the other, and can wait until you kill others or lynch others or others claim to narrow it down.
Method 2:
If the 2 commuters are already dead, for example, by the lynch
the remaining resistant people will be bulletproof. And this is true, vice-versa. While you didn't know
for sure at the start of the game how many of each there were, if a bulletproof person dies, the odds are better that any other resistant person will be a commuter. If two bulletproof persons die, it's essentially a lock that anyone else with natural resistance will be a commuter or they just happened to be protected by a doctor that night. And since the doctors are almost always vulnerable to your regular shots, sweeping with the vanilla shots might eliminate them from the game early. Doctors who are forced to claim might also reveal who they protected on a night that there was a missing kill, and you'll know if they were even protecting the person who didn't die, usually revealing a commuter or bulletproof in that slot.
-----------------other thoughts-
If you simply guess, you have a 50/50 chance of being correct anyway. Guessing when you have only encountered one person with resistance is probably a waste of time, it's better to use the normal kills to locate murder-resistant people, like an investigation.
If you only have one known resistant, it's better to keep sweeping. But, suppose there are 3 known people with resistances to your normal kills, and they haven't revealed which resistance it is. Even with no additional knowledge:
The game started off with dead commuter d1, which meant that the odds were pretty good anyone who was resistant thereafter was a bulletproof.
Example, when you hit Cass that one night early on, you found a bulletproof.
So suppose you took a night at shot at Cass with an anti-bulletproof shot. She would have died outright, or, she would have been very likely to be commuter. Then you would have knowledge of who both of the commuters were, one dead, and one alive but found out. And then, any
other persons who had resistances would be easy to assume are all bulletproof, or the informant.
Those assumptions are easy enough to make that the addition of limited doctors and a murder-resistant member of your team was intentional, so as to still make it a bit of a guessing game.
Doctors are unlikely to be the reason why someone is resistant to death, because those passive resistances are effective every single night for that target, and a doctor has a chance of protecting a mafioso and thus not influencing the game at all, or has a chance of protecting the other doctor, which does absolutely nothing, or might be protecting someone you're not murdering.
They become powerful if they're still alive in the late game and the odds are higher they're protecting a vanilla townie that you're shooting. But in the early game, they had almost no influence on the game and could only get extremely lucky.
The bulletproofs and the commuters (2 each) were the most likely reason why someone didn't die if you shot them, and as they died, claimed, or were revealed by some method (random vanilla shot sweeps, or a concerted 50/50 shot, you shoot them and they live or die, gains some information that way)
It's especially solving if there is one dead commuter or bulletproof already. Then almost anything you do to try to take down a resistant person tells you valuable information. If you try to aim for the other remaining example of that power, and they don't die, you've narrowed it down to them being very likely to be one of the examples of the other power. If they do die, you basically have it locked that the other two resistant people are both the other kind of resistant power, or you've located your informant which is very helpful to you.
You probably won't try very hard to lynch someone who you have determined is either one kind of resistant power or the informant.
A lot of the approach above relies a bit on playing the waiting game.
The vanilla shots being deflected tells you something, that they hit a protected person or a resistant person, and it will usually be a resistant person.
Flips and claims should give you enough additional information that even one 50/50 shot at a resistant person has a decent chance of murdering one, and completely solving the rest.
It's not 100%, but there are processes of elimination and deduction, the advantage of knowing a lot about these powers because you were provided with their role information at game start, and claims and lynches to help you narrow it down.
If you decided to chance things early and use one of your special kills on someone you know to be resistant to murder, it's still in the early stages where the odds are lower that the town can guess who you are with the lynch vote, so a missed kill at that stage of the game is less threatening to your odds of winning.
If you hit the target and kill them, you reveal one of the resistant townies and make it very simple to solve the others. So even if one of them didn't die early by the lynch, it's relatively easy to find a resistant person and try to take them out with a 50/50 shot very early with very little risk if the result ends up being no murder that night.
That's what I thought about when designing the game, and although you didn't know the exact setup, you began with enough information I feel to be able to come up with a strategy of tackling this problem which would be better than blind guesses, and can probably solve it with a likely maximum of one incorrect guess.
With the slight additional variables of the informant and a weak doctor you didn't know about with a one-shot super protection, it meant there was a slight chance that you could make all the right assumptions and still miss more than once, but I felt the odds were low enough that it doesn't undercut the general utility of those assumptions.