What globel event is triggered on saving the 'Form' tab of a custom page type?

The ask: we have a custom page type with a checkbox we'd like to synchronize across the different language versions of a page.

e.g. Admin user goes to page type in admin tree view, checks the box on the English page, we'd like to synchronize that selection across the other languages as well.

I thought our best answer would be to capture the checkbox being updated via global event handlers and to process the checkbox for the other language variants at the same time. I feel like this should still be feasible but I'm having trouble capturing any events on update of the checkbox on the 'Form' tab.

Steps I've taken: I followed (https://docs.kentico.com/k11/custom-development/handling-global-events/handling-object-events) to make a module that I can confirm the OnInit is hit (via breakpoint running locally) and I have confirmed that other events fire on page load (ObjectEvents.Update.Before) but when checking the 'Debug' tool with 'Event Handlers' turned on I don't see any interaction when saving the given page with the 'Form' tab visible in the 'Page' tree view. I expected the DocumentEvents.Update.Before event to trigger on save but it doesn't seem to.

Any advice on process or guidance on how to properly trigger an event would be appreciated. Perhaps additionally if there's a simple code behind way to grab the other language versions of a page for future reference that would also be appreciated.

Class created (the 'data' lines are just to give something for a breakpoint to hit as a proof of concept):

using System;
using System.Collections.Generic;
using System.Linq;
using System.Web;
using CMS;
using CMS.DataEngine;
using CMS.DocumentEngine;
using CMS.Helpers;
using CMSApp.Helpers;

// Registers the custom module into the system
[assembly: RegisterModule(typeof(LanguageToggleSyncModule))]

namespace CMSApp.Helpers
{
    public class LanguageToggleSyncModule : Module
    {

        // Module class constructor, the system registers the module under the name "LanguageToggleSyncInit"
        public LanguageToggleSyncModule() : base("LanguageToggleSyncInit")
        {
        }

        // Contains initialization code that is executed when the application starts
        protected override void OnInit()
        {
            base.OnInit();

            // Assigns custom handlers to events
            DocumentEvents.Update.Before += LanguageToggleSyncBeforeUpdateHandler;

            DocumentEvents.Update.After += Update_After;
            DocumentEvents.GetData.After += GetData_After;
            ObjectEvents.Update.Before += Update_Before;
        }

        private void Update_Before(object sender, ObjectEventArgs e)
        {
            var data = 1;
        }

        private void GetData_After(object sender, DocumentDataEventArgs e)
        {
            var data = 1;
        }

        private void Update_After(object sender, DocumentEventArgs e)
        {
            var data = 1;
        }

        // ensure the "Show Language Property" is synced across both english and spanish version for "Agency Office" page types before saving them
        private void LanguageToggleSyncBeforeUpdateHandler(object sender, DocumentEventArgs e)
        {
            if(e.Node!= null)
            {
                var docClassName = e.Node.NodeClassName;
                //confirm working with an agency office page type being saved
                if (docClassName == "custom.AgencyOffice")
                {
                    var agencyOffice = e;
                }
            }

        }
    }
}