Rules for reacting to Run Pipeline button in Merge Request

We would like to restrict running certain pipelines to active triggers - ideally via pushing an already existing button in Gitlab. Now I was surprised to find out that the button under
Merge Request → Pipelines → Button: “Run Pipeline”

creates a “merge_request_event” as $CI_PIPELINE_SOURCE instead of a “web” event. Apparently really only (as per the doc) the button Build > Pipelines triggers the web event.

Is there another possibility (CI pipeline attribute?) for filtering out the “Run pipeline” button event from the Merge Request? I’d like that no updates on the MR trigger the pipeline and only the “Run pipeline” button does.