How to check if a certain column in gridview has an empty row and be able to perform an action

Convert your ButtonField to TemplateField column so you can have a control over the controls within it:

<asp:templatefield>

The at RowDataBound event, you could toggle the Enabled property of the Button based on your requirement. A quick example would be:

protected void GridView1_RowDataBound(object sender, GridViewRowEventArgs e)
{
      if (e.Row.RowState != DataControlRowState.Edit){// check for RowState
              if (e.Row.RowType == DataControlRowType.DataRow){ //check for RowType
    
                     // Get the signout value
                     // Note: You may need to change the index of Cells based on the column order
                     string signoutDateString = e.Row.Cells[0].Text; 

                     if(string.IsNullOrEmpty(signoutDateString)){
                            //assuming your Action Column resides within the 5th column
                            //access the LinkButton from the TemplateField using FindControl method
                            LinkButton lb = (LinkButton)e.Row.Cells[4].FindControl("lnkSignOut"); 
                            if (lb != null){
                                 lb.Enabled = false;
                            }
                      }  
               } 
        }
}