Instead of creating an instance of a new Form, you probably need an instance of already opened form and call the method from there. You can try:
if (System.Windows.Forms.Application.OpenForms["yourForm"] != null)
{
(System.Windows.Forms.Application.OpenForms["yourForm"] as Form1).Output();
}
plus you can replace calling the button3_Click(null,null)
in your Output
method, by placing the code of the event in a separate method and then calling that method against your button click event or your public output method