Despite having this in the config file:

{
        "KillerType": "Player",
        "VictimType": "Player",
        "DamageType": "Suicide",
        "Enabled": false,
        "Messages": [
          "{victim} had enough of life."
        ]
      },​

See how you have enabled set to false? That prevents that death message from working and then it's moving on to the next death message that fits the situation. Try setting enabled to true on that. If that still doesn't work, send me your DeathNotes.json file via Discord (@terceran.) .

Hey Terceran, I think you misunderstood my issue.

"Enabled" set to false SHOULD prevent the death message from working.
I don't want that death message to work.
That's why I set it to false.

But as you can see in the screenshot, despite having it set to false, it's still displaying a message when a player kills themselves.

Sorry, I thought you were trying to enable it, because the death note you sent the screen shot for isn't what is printing to your logs. If it had, you would have seen "LEON had enough of life". Another death note is hitting, and printing that "LEON killed LEON using their ." message. If I were to guess, there is probably a Player KillerType, a Player VictimType, and a "*" (everything including suicide) DamageType that is firing.

Indeed I had a Player/Player/* 

I thought it was needed as a "catch all" but will turn it off.
Thank you for your help :)

Sure thing! '*' is in fact a catch all. When you disabled the other suicide message, it then went further down the line and saw '*' (which means all DamageTypes), so it used that Death Message. Otherwise, if the Suicide one was enabled, it would have used that first. Hopefully this helps. Thanks again.