You can use the RingCentral push notification API to subscribe for the fax events.

'/restapi/v1.0/account/~/extension/~/message-store?type=Fax&direction=Outbound'

When you receive a fax event, you can check the newCount value to see if there is a new outbound fax message, then keep the message id from the newMessageIds. If the updateCount > 0, use the message id to read the message status to see if the fax was delivered or failed.

'/restapi/v1.0/account/~/extension/~/message-store/omessageId]'