I struggled to add both click events to the string binding string:
e.Row.Attributes.Add("onclick", ClientScript.GetPostBackClientHyperlink(this.gvMainGrid, "Select$" + e.Row.RowIndex));
e.Row.Attributes.Add("onclick", "onGridViewRowSelected('" + e.Row.RowIndex.ToString() + "')");
Adding the PostBack method after selecting the line selection method with ;; seems to have worked.
e.Row.Attributes.Add("onclick", "onGridViewRowSelected('" + e.Row.RowIndex.ToString() + "');" + ClientScript.GetPostBackClientHyperlink(this.gvMainGrid, "Select$" + e.Row.RowIndex));