I found my error! I never used Begin MYPEONYP in the initial dialogue file. This brings me questions.
Why is a *P file needed if the text for parting is in the *D file?
I noticed when I used NumTimesJoined(0) the character infinitely loops their clicking dialogue while in the party, as if trying to initiate conversation again. Is it because NumTimesJoined(0) is never set to 1, and where would you set it to 1 at?