The docker image I use on the Pi4 didn't build on the Zero, so I had to instead do a scripted install.
The base of the instructions came from here; https://forums.plex.tv/t/suggestions-for-the-future-headless-rpi-support/218187/56
You must get a server.json file from existing Plexamp install and put it in the same folder as this script before running.
Sign out and back into your existing install to get a new identifier/token.