What observations would lead you to believe that the ink is actually a mixture?

You can check that ink is a mixture by using a filter paper chromatography to separate ink.
You will notice that the dark ink is actually composed by mixing other ink colors together. The number of ink colors used increase as the output ink gets darker.

Based on the observation that darker ink is actually composed by mixing other ink colors together leads to the conclusion that ink is actually a mixture.

They are like other investigations? say there was a murder u have to do blood test and finger prints which run through a lab.