I would love to see your prompt if you ever post it anywhere.

For Claude, it's enough to prompt "use tmux to test", that usually does the work out of the box. If colors are important I also add "use -e option with capture-pane to see colors". It just works. I used it regularly with Claude and my TUI. For other agents other than Claude I need to use a more specific set of instructions ("use send-keys, capture-pane and mouse control via tmux" etc.)

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"