For example
Obito (Kamui ) unlocked after obito saw the tragic death of rin. Obito's mindset/will was to "escape" from the horrible reality of the ninja world which is basically wat kamui ables the user to do , "escape"
Itachi (Tsukuyumi , Amaterasu , Sussano'o ) unlocked after seein death of shisui.
Itachi was a pacifist with a higher mental understanding than all shown uchiha , his keen intellect was noted many times and as such his mastery of (Tsukuyumi ) is a given , due to his godly intellect and calm as water mindset.
Tho calm itachi also carries "the will of fire"(Amaterasu ) which respesents his nature elements perfectly "Water , Fire" , Fire represents (Ama ) while Water represents his (Tsukuyumi ). Itachi's amaterasu repesents his burning will to protect whats truly dear him (konoha , sasuke ).
"Susano'o" is simply a physical manifestation of the users burning will given form through chakra.
Shisui (KA ) unlocked by unknown means , tho it can be argued that due to shisui's power to "control" the will of others its possible that shisui unlocked MS due to lack of control of the certain events that trigered the awakening of his MS , possible related to the death of his father kaname.
Shisui's mindset/will was to protect his village/clan at all cost , even if it meant to sacrifice his own flesh and eyes for the sake of those dear to him , he showed no qualms with controlin others if he feels thats its best for everyone as a whole. Itachi also shared this quality as he had no problem controling sasuke if he strayed to the wrong path and became a threat to everyone.
The death of shisui was a very symbolic end for a man who had the ultimate form of "control" at his finger tips.
Sasuke (Amaterasu , Enton , Susano'o )
Unlocked after gettin blasted by the horrible reality of losin the people he loved dearly.
It stemed a burning need for vengeance and hatred which nearly drove him mad.
Amaterasu respesents the burning hatred he felt towards those responsible and "enton" represents the power to control the power of his vengeance , mold it into any shape/form and used to incinerate any who gets in his way.
This power firmly fits all forms of sasuke from MS to current , the power to control his vengeance and turn it into a great flaming sword used to cut down enemies and protect those he loves.
Sasuke himself is a true respesentation of the "will of fire .
Susano'o is simply a physical manifestation of the users will given form through chakra gained from the awakenin of MS.
Its possibly the reason why madara had such large and destructive PS as his will was always to stand at the "top" which stemed from his will to become the strongest and to protect those he holds dear.
This can be seen in his battle with hashirama after ge coated kurama with PS.
Same with indra who believed that "might" was the ultimate way to achieve peace.
This can also be the reason why obito struggled to control the juubi while madara simply owned it with zero diff , it respesents the difference in their power of wills and their respective abilities.
Madara simply stood above and overcame the juubi while obito had to connect back to wat was dear to him (rin ) which ultimately gave him control of the juubi and ultimately led to his defeat at the hands of naru/sasuke due to his waverin will and doubt.
By reconnecting his feelings to the memory of rin he began to realise that the "escape" he desired in the form of infinite tsukuyumi was possibly just one big lie and would in the end do no good at all , which resulted in the sword of nunoboko breaking
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