Notify when database is accessed in any manner
To clarify, it's actually one particular table I'd like to monitor 


You should use SQL Database Audit.

Below is an example that you are looking for (based on your comments)

(Modify as per your criteria and needs)

CREATE DATABASE AUDIT SPECIFICATION [AW_Audit_HR_Employee_DML]

FOR SERVER AUDIT [Server_Audit_AW]

ADD(SELECT,INSERT,UPDATE,DELETE,EXECUTE ON HumanResources.Employee BY sys)

WITH (STATE =ON)


More info at : SQL 2012 Security Audit 2 (Database Audit)