Is there a way to manually reset the ink level sensor on an HP Ink Tank 410 series printer when experiencing error 4?

Yes, a manual reset can sometimes resolve error 4. The procedure varies slightly depending on the model, but generally involves holding down the 'Stop' button for 10-15 seconds after powering on the printer. Consult the HP Ink Tank 410 series printer manual for the exact manual reset instructions for your specific model number.