I think the term “NPC” fits him like a glove.

I never specifically thought about him until Darth Vader 2017, Issue 19. I won't spoil what happens for anyone who hasn't read it, but it obvious contains Vader, therefore nothing good happens.

After that issue, I found Eeth Koth really karking stupid. Honorable, but stupid. I also agree with @Darth Cumulonimbus that the guy is just kind of sometimes "there". He's always on the sidelines no matter how cool or good he's meant to be, and he adds only tiny bits to the story that could have been served by basically any Jedi.

Apparently, in Legends, Koth was well known for his successful training of Sharad Hett, who went to become one of the most respected and famed Jedi Knights at the time.