Mutsuki have habits that a little like kaneki, when he was hiding something. the different is mutsuki would squeeze his shirt. i don’t think he was lying but he just hiding something or just unsure about something.
there a lot panels that show Mutsuki squeeze his shirt (im sorry if i miss something) :
1) when he was asked by shirazu about what’s wrong with haise
2) when he called cute by haise
3) when he was asked to become an investigator
4) when he was asked about what happened to his family
5) when he said that the person who kill his family is a ghoul
and i think mutsuki itself doesn’t know his own habit.