I can successfully start the SQL console client using this command:
docker exec -i $ELASTICSEARCH_CONTAINER_NAME /usr/share/elasticsearch/bin/elasticsearch-sql-cli
However, I ran into a problem with the proper terminal environment not being passed down to the console program, so I didn't have readline support (no up and down arrows, etc.).
I posted a question on this and then immediately came across the fix:
docker exec -it $ELASTICSEARCH_CONTAINER_NAME /usr/share/elasticsearch/bin/elasticsearch-sql-cli
That "t" after the "i" makes all the difference.
I hope you find this useful. I am a total noob to Docker exec functions, so it took some pain for me to discover this.