I’m not that familiar with external tasks. However, and what follows may be obvious so I apologize if it is, if Camunda is tracking, using, or establishing some sort of relationship, with any “object”, it is stored in the Camunda database. The REST API often is just an easy access point for an underlying SQL query.
Not all information one might require is accessible through a REST API method, so you might need to derive this information via a direct SQL call. We don’t use external tasks at this time, so I can’t be sure, but it would appear that the ACT_RU_EXT_TASK table might contain the information you’re looking for.