What the problem is
The key error in the above was is WriteOnly. When you are referencing columns in Script Components as Transformation, you can specify whether they are ReadOnly, ReadWrite.

When acting as Source, you don't have that option. It's WriteOnly (logically) and they don't even give you the option of the above dialog. So, when you're in your Source and attempt to access write only properties like the following code demonstrates, it breaks.
Public Overrides Sub CreateNewOutputRows()
Output0Buffer.AddRow()
' this is logically wrong
If Output0Buffer.Column_IsNull Then
End If
End Sub
The resolution is that you need to inspect whatever you are assigning into OutputBuffer0.Column prior to making the assignment (or create a separate boolean flag) to keep track of whether the current value was populated.
What the problem isn't
Keeping this here since I already ran down this rabbit hole
Since _IsNull is boolean, you can skip the explicit test and simply use
If Row.Column_IsNull Then
Originally, I had thought this was the classic C-like language issue of assignment (=) vs equality (==) but as @John Saunders was kind enough to point out, this was VB.
That said, the supplied code should work (it does for me).
Public Overrides Sub Input0_ProcessInputRow(ByVal Row As Input0Buffer)
Dim x As String
If Row.Src_IsNull = True Then
x = "" ' do nothing
End If
End Sub