Fkelly
hello there is no heter to be mechallel Shabbos in any way without the proper guidance from a competent Rav.
As per a case of mental health that a person is in danger if music doesn’t get turned on the heter would be amira leakum betrei drabannons bemokom mitzvah .In the torah we learned vechai bahem velo sheyomos. Let’s talk about the situation here at hand he would not be in the army if he had a mental issues . He has nisyonos he needs to overcome them I am not telling him to overcome them the Torah says ubocharta bchaim choose life no just the life wich goes by in a flash 60-70-80 if u r lucky but eternity eternity remember time is a creations of this world hashem will remove time one day and those that will merit will has eternal bliss.