It might be possible to permanently disable Function Lock in the UEFI Firmware Settings. Shift + Click the Restart button, Troubleshoot, Advanced Options, UEFI Firmware Settings. Use the arrow keys to switch tabs until you find Function Lock, highlight Function Lock, press Enter, switch to Disabled, and press Enter again. Exit Saving Changes from the Exit tab.
If that is not possible, use Task Scheduler to create a task instead of using startup items. Open Task Scheduler as administrator and click Create Task. Change the task to run under the account Administrator, whether the user is logged on or not. If necessary, check the box for run with highest privileges. Create a new trigger for At Startup. Create a new action and input the path to the "Function key main module" file. Uncheck the box for only AC power, under the Conditions tab. Click OK and click Run in the sidebar to test it.