Garret,
Sorry for the slow response. In order to accomplish this, you need to create the Custom Workflow Rule at the Project Customer Link Item type. Your Evaluation criteria would be based on the change on the Project in the for business code. For example...
If True =
isChanged($Project.C_BusinessCode)
Then the Action would be Update Field and the Field updated would be the corresponding business code field at the Customer item type.
For further clarification, we suggest you register for one of our Advanced Q&A webinars (see the link-> http://www.clarizen.com/resources/online-demo.html#second ).These are great resources for free consulting with our Customer Success Managers and visual answers to your questions.
Sincerely,
Boris