Offset does not skip locked cells

Following does as designed - moves one cell to right on noted worksheets.
BUT - i want it to move right to the next unlocked cell after an entry.
What change needs to be made?
Thanks

Private Sub Workbook_SheetChange(ByVal Sh As Object, ByVal Target As Range)
Application.EnableEvents = False
If ActiveSheet.Name = "Payroll Wk 1" Or ActiveSheet.Name = "Payroll Wk 2" Or ActiveSheet.Name = "Payroll Wk 3" Or ActiveSheet.Name = "Payroll Wk 4" Then Target.Offset(0, 1).Select
If ActiveSheet.Name = "Equipment Wk 1" Or ActiveSheet.Name = "Equipment Wk 2" Then Target.Offset(1, 0).Select
Application.EnableEvents = True
End Sub