Since GridView1 uses SqlDataSource2, what you want to do is update and rebind SqlDataSource2 everytime you search. My code isn't exact as I didn't test it, so make sure you go through it yourself.
In your Search button click event, update the datasource, and then rebind.
protected void Button1_Click(object sender, EventArgs e)
{
SqlDataSource2.SelectCommand = "SELECT * FROM People WHERE Person_Type=" + DropDownList1.SelectedItem.Text;
SqlDataSource2.Select(DataSourceSelectArguments.Empty);
GridView1.DataSource = SqlDataSource2;
GridView1.DataBind();
}