The /conversations endpoint also has a waiting_since field as timestamp (link to API ref)
waiting_since
Coverage increased (+0.01%) to 95.845% when pulling e23e7498142df573fb6cb48ce183dcb3ccfcd541 on mikexine:master into abcc2722fc46a5832c9d2b56adc99ac7f4d4b206 on jkeyes:master.