I'm having the same problem which has not been answered by in the Quickbooks team response above.

nyba225 specifically stated in the subject and body of the question that the solution needed to avoid using the Payroll Mapping tool as that resource is not available without additional subscriptions.  The Quickbooks team response states, "Otherwise, you can manually assign payroll items for each employee." which would mean there is an answer to the question nyba225 raised.  In attempts to resolve the issue using a manually assigned option, this, too, appears to be a dead end in recent QB updates. 

Please provide a specific resolution and instruction how to "manually assign payroll items" in order to use QuickbooksTime without a Payroll subscription.