Then just prompt Claude to "use tmux to interact with and test the TUI rendering", prompt it through anything it gets hung up on (for instance, you might remind Claude that it can create a tmux pane with fixed size, or that tmux has a capture-pane feature to dump the contents of a view). Claude already knows a bunch about tmux.
Once it gets anything useful done, ask it to "write a subagent definition for a TUI tester that uses tmux to exercise a TUI and test its rendering, layout, and interaction behavior".
Save that subagent definition, and now Claude can do closed-loop visual and interactive testing of its own TUI development.
Since I have e2e tests, I only use the agent for: guiding it on how to write the e2e test ("use tmux to try the new UI and then write a test") or to evaluate its overall usability (fake user testing, before actual user testing): "use tmux to evaluate the feature X and compile a list of usability issues"