Starting with the base word, zeal:
The AHDEL gives a definition which is positive if anything (rather than pejorative):
Enthusiastic devotion to a cause, ideal, or goal and tireless diligence in its furtherance.
Collins adds the pejorative flavour:
Fervent or enthusiastic devotion, often extreme or fanatical in nature, as to a religious movement, political cause, ideal, or aspiration.
My own take is that the connotations are positive rather than negative.
Zealous has the same effect on my sensibilities. At least one version of the English Bible contains 'zealous for good works'.
Zealot, however, perversely seems to connote unwarranted fanaticism. Simon was a zealot before his conversion (and a Bible interpreter I know of suggested that that's how two swords could mysteriously appear among the disciples just prior to the Crucifixion).
It's not unknown for closely related words to have very different connotations - contrast:
Thank you for preparing this excellent scheme of work.
I wouldn't trust him - he's a real schemer.