I finally got it working.

From a server, under IIS, I can enable/disable a task from the Windows Scheduler as well as starting/stopping the execution of that task on a remote server. This requires the application pool identity to be changed to the same account as the one in the Windows Scheduler for the RunAs field. So, we just have to synchronize those related tasks to use the same username and password for the RunAs as the one defined in the application pool identity on the IIS server triggering the hit.

Now, what is confusing is that the enable and disable option requires /ru and /rp for the username and password. However, to end and run the task, you need to use the /u and /p options.