VBA Updating For Manual Cell Entries But Not Automatic Ones

I have in cell A2 a number, and my VBA is as follows;

If Target.Address(0, 0) = "A2" Then
Application.EnableEvents = False
Range("a" & Rows.Count).End(xlUp)(2).Value = Target.Value
Application.EnableEvents = True
End If

This basically adds any new number typed into cell A2 into a list which starts in A3 then continues down through column A.

I also have another part of my VBA which says;

If Target.Column = 1 Then
Application.EnableEvents = False
Cells(Target.Row, 2).Value = Date + Time
Application.EnableEvents = True
End If

This part works fine and adds a date stamp to my blank cells in column B whenever I manually type anything into column A, however, when the first part of the VBA works the date stamp is updated into cell B2 and I want it to update next to the new entry that has just been added into column A by the first VBA doing its job.

I think I need to change;

Cells(Target.Row, 2)

To something that refers to a Range of cells (would be B3-B5000 for example) but my knowledge on how to change that part of the VBA has now ran out!!