Either method should work, but a scheduled task is probably easier and
won't require a 3rd party service wrapper.
You'd want to configure a task to start globus_connect_personal.exe at
startup, run as your GCP user, set to "whether user is logged on or
not". You should not need to store the user's password, but that may
depend on the version of Windows, or if it needs to access network
drives. Check the additional settings to ensure the task won't be
killed after a time limit.
Before that is set up, you can disable the GCP setting to start
automatically, otherwise it would complain that another instance is
running. Any configuration changes would require terminating the task
and running normally under your GCP account.
Mike