Is it possible to have a global minor mode disabled whenever a certain major mode is enabled?

[James Gregory]

I have a global minor mode (highlight-symbol) that conflicts with a
major mode (js2-mode). I have seen an alternative implementation of
highlight symbol that doesn't conflict, but it has some issues of its
own. I would rather just disable highlight-symbol whenever js2-mode is
loaded, but I can't work out how to do this.

I have some code like this in my init files:

;make it a global mode, and switch it on
(defun highlight-symbol-mode-on ()
  "Turn on function `highlight-symbol-mode'."
  (highlight-symbol-mode 1))

(defun highlight-symbol-mode-off ()
  "Turn off function `highlight-symbol-mode'."
  (highlight-symbol-mode -1))

(define-globalized-minor-mode global-highlight-symbol-mode
highlight-symbol-mode highlight-symbol-mode-on)
(global-highlight-symbol-mode 1)

(add-hook 'js2-mode-hook 'highlight-symbol-mode-off)

///

But though the hook at the end is called, highlight-symbol is still
switched on in js2-mode buffers. I guess this might be because the
global minor mode is enabled after js2-mode has already loaded? Or
some other load-order issue.

Thanks,

James