Hi David,
For your purpose, please try to use audit policy to record the DB connections.
Choose audit trail target to database tables, so you can later query the information you wanted.
For more informtion, please refer to SAP HANA security Guide (Link of SPS 12 http://help.sap.com/hana/SAP_HANA_Security_Guide_en.pdf )
Regards,
Ning Tong