i think here in the forum are examples of UI scripts, that would trigger tests from TestRail to an automated system.
But the general approach and/or suggestion is, that the CI system should be the active part here. It knows, when things have changed and can then start the tests and then post the results to TestRail. This would be a full automated system.
When you trigger the test execution from TestRail, it is a manual step, where you need to know “ah now something has changed, let’s start” - so I do not see any gain from this approach and it is not fully automated
this might help: http://docs.gurock.com/testrail-custom/automation-trigger