ExecutionMode switches between one-shot and long-running. The RESULTING mode+schedule are validated together, so switching to long-running without a stored or supplied cron is refused rather than accepted into an agent the scheduler would skip forever. A switch INTO long-running counts against the per-org cap and can be a 409.
Model re-points the agent at another model, checked against the gateway's served catalogue exactly as create checks it. Empty STRING is refused — say nothing to keep the current one. Past runs keep the model that served them.