I haven't used a pump in years, but then, my site isn't yours. I recently added ducks to the equation and I'm reconsidering my set up. I'll be increase my pond size this spring, adding a solar pump, and a natural bio-filter.
Forgive me if I missed the part of the thread where you give more details, but if your site is warm at night, lacks shade, etc, has few to no plant coverage, I would recommend 24/7/365. If your pond cools off at night, you have shade, pond plants, etc, I wouldn't worry that much about it.
Best wishes