Does it make sense for customer marketing to live inside of the product marketing team? If so or not, why?

Great question! I have seen customer marketing both within PMM and outside of it. Depending on the organization, it could work either way as long as product and customer marketing work very closely together. 

To ensure success, I would suggest that customer marketing be part of product marketing for many reasons. PMMs are expected to be experts on customers and are usually the ones that either lead or highly influence customer-related activities such as: 

• Increasing product adoption
• Content for customer events
• Win-loss analysis
• Customer stories/case studies
• Customer communications, specifically about best practices and feature launches
• Advisory boards
• Etc.

When customer marketing and PMM work together and there are no silos, then the customer experience improves. A win-win situation.