cscript prnqctl.vbs -e [-s ServerName] -p PrinterName [-u UserName -w Password]
In this case, you need to know how to schedule the test print via Task Scheduler. Here are the critical pieces of info.
Action: Start a program
Add arguments: %WINDIR%\System32\Printing_Admin_Scripts\en-US\prnqctl.vbs -e -p "My Printer Name"
Set the task to run however often you'd like and under whatever condition you prefer. Those may vary based on whether your PC is set to sleep/hibernate and other factors.
If at first you don't succeed, fear not. Google is your friend. Now that you know "prnqctl.vbs" exists, the finish line is within sight.
*To those who have answered such queries with snarky comments about buying a laser printer, "go suck a lemon." - Barry Kripke from Big Bang Theory.