I think the question is the substitution effect. If easy access to firearms really did increase the total number of suicides by a substantial amount (i.e. they were more effective, or people were not willing to use other methods), then I'd view it as something specific to firearms.
I'm pretty sure there is near 100% substitution, but that firearms are a much more effective method, which accounts for the net difference.
Having a gun around is a constant reminder of death in a way that having a rope or a drawer full of kitchen knives is not. The objects in your environment are directly related to the choices available to you and are part of the framework you use when trying to think about what actions to take.
Clearly false: In Switzerland, even though one likely posses a gun, one is more likely to use a rope to commit suicide.
While we, being simple humans, may project feeling upon an inanimate object, it's a mistake to assume a god's eye view, objectivity, or universal reality.
Bringing it back around: Are you suicidal? We're here to help. ;)
I am not sure that you fully understand my point as the method used is not what I was getting at exactly. Even if the majority of people do not reach for the gun as the method does not say whether the availability of the gun made the suicide more likely. It also matters what you associate with the gun, you could have very different thoughts about a gun kept for hunting deer, than one kept for shooting potential attackers, for instance.
I read your argument as (1) humans are entangled with the environment and (2) a judgement that guns are related (mind) to death more so than edged weapon or rope (hence my question of your mood or state). Following your logic, shouldn't we expect a higher rate of suicide in Switzerland than the US?
As for intentionality, proper reference to cultural symbol and relation, as you state in your last sentence, is essential but seemingly ignored in favor of how one believes, desires.
The Golden Gate Bridge might be a well studied form of this (it's a fairly common suicide location, and a visible landmark across much of SF). i.e. do people commit suicide more frequently if they have a view of the GG Bridge vs. a view of something else?
I'm pretty sure there is near 100% substitution, but that firearms are a much more effective method, which accounts for the net difference.