How do I assure that mouse pointer appears when mouse moves over form after commanding the drop down for a combobox to show?

As already commented to the question, the issue is not Delphi related. You can observe the same behavior in dialog boxes which contains a similar combo that the OS presents. One example is the one on the "run" dialog.

Involving a single environment, re-setting the cursor in an OnDropDown event handler fixes the problem.

procedure TForm1.ComboBox1DropDown(Sender: TObject);
begin
  winapi.windows.SetCursor(Screen.Cursors[Cursor]);
end;

Originally I tested the above because no one calls SetCursor after the drop down. Though it seems that no one calls it before either. So I have no idea about the cause or why the above fix works.