I remember an old Charles Addams cartoon, a woman comes home and finds her husband hanging in the closet. He managed to get his arm and head in the noose and did not die.
She says...."For heavens sake John, can't you do anything right?"
Then there is this young man. No guns or nooses needed.
Anyone who successfully kills themselves with a gun is likely to have killed themselves by other methods if a gun wasn't available. A firearm is quick and reliable but so is hanging or jumping from a building or bridge if the distance is adequate. I would imagine the guillotine in your illustration is very quick provided it is heavy enough to cut cleanly through the spine.
The question is: Should firearm suicides be placed in the same category with other gun homicides?