Macro to copy non adjacent cells to external workbook and move down row

You might have to go with this. I'm not sure the correct syntax for using 'Destination'.

Worksheets(SourceSheet).Range("Call_Number").Copy
Workbooks(ExternalWorkbook).Sheets(TargetSheet).Cells(Rows.Count, 1).End(xlUp).Offset(1, 0).PasteSpecial Paste:=xlPasteValues