I was also told same by the customer service rep to call back towards end of the testing period.Majority of recent applications have been getting processed at a much quicker pace. When I called IRCC they literally said to call them at the end of the exam period if exam hasn't been updated.
There is nothing wrong with shooting an email and if the agent feel like it they might reply.
I do have a question about it. My testing period ends on 2nd Jan. Considering the holidays will it make sense to call this Friday? Or mid next week. Any suggestions?