Chalk this up to needing to take a step back. You're right, I did not need to be using during the headless render. I should have been adding it when the server-side code is hydrated with the client-side code.
If anyone comes across a similar problem, I was able to load the plugin successfully by adding the following to my nuxt.config file:
build: {
extend (config, ctx) {
if (ctx.isClient) {
config.entry.app = ['gsap','~plugins/DrawSVGPlugin', config.entry.app];
}
}
}