When should I be changing the 12V battery? 2015 prius c <39,000 miles

That's killing your 12 volt.

Time for a new battery. If you want to confirm, have it tested with an electronic load tester. Stores selling batteries will often have these, and will test for free. Or you can DIY test with Solar BA9 or similar. If it comes up with CCA below spec (say under 300), it's time. The tester will let you know the voltage, measured CCA, and typically give a verdict, if it's viable or not.

 

does the dashcam shut off with the car?

 

^ Set your dash cam thus, get another battery, you’ll be good. You don’t want to lumber the diminutive battery with anything extra.

 

Keep in mind that the car does a number of post-shutdown tests. Some of them are scheduled to occur hours after shutdown.

These tests involve actuating valves and pumps, so they use electricity. Not a lot of electricity, but it is measurable. Meaning, the overall system voltage may be appropriately dipping down due to the load of the tests being performed.

If the camera sees 11.5 and the car starts a purge valve test *boop* maybe it's down to 11.4 for a second, the camera calls it a night, the test finishes and the voltage bounces back up afterwards.

...but the better answer is that 8 years is a great run for one of those 12v batteries. You got your money's worth, now it's time for a new one.

 

Yep, any load will drop it. You'll often hear one of the pumps humming away.

I'm still on my original from 2012, but I got a new one to replace it anyway when I do the hybrid battery too.

 

100 Amp, 6/12V Battery Load Tester