the Israeli military did a study about ~15 years ago where they looked at soldier suicide rates after they had enacted a policy of leaving the weapons at base over the weekend and if I recall correctly it cut the rate of suicides by 40-50%.
The US Veteran's Affairs agency makes a free app to help with insomnia; it has all the usual advice that would apply to anyone - plus advising veterans not to keep a loaded gun by the bed, even if it makes them feel safer going to sleep.
I bet that has as much to do with where and when alcohol is consumed as it does guns.
And on the flip side, the US Sec Def recently allowed US soldiers to carry loaded weapons on base (when not in a role that required it, which was previously disallowed). I expect this will increase suicides on US military bases. All for some "rah rah, 2A, mah rights!!!" bullshit political posturing.