With some help from crythias over at the OtterHub forums, I was able to find the right setting.
- Navigate to the SysConfig
- Filter by the Ticket config group (dropdown on left)
- Locate and select Frontend::Agent
- Locate Ticket::Frontend::DynamicFieldsZoomMaxSizeSidebar
By default this is set to 18 characters. I reset it to 140 (Twitter rules), and it automatically wrapped the text for me.