AFAIK none exists. Closest thing I can think of is a bottle dynamo setup. Both lights wired to the dynamo. When one is lit, the other should be too. Although while bottle dynamos can be engaged while riding, I don’t think I’ve seen one that disengages easily while riding.
There are a couple of fairly good reasons why your dream system doesn’t exist:
-an indicator isn’t proof. As a cyclist you're expected to be able to monitor traffic behind you anyhow. If you can do that, you can check if your rear light is working. Turning your head is more reliable and require less installation on the bike.
- the power consumption of LED-based rear lights is so low that there’s very little practical benefit from toggling them on/off mid-ride.
-cabling. Unless you want a wireless system, you’d need to run several wires back & forth along the bike. And given the low voltage most likely used on bicycle lights, the contact resistance at every point becomes important. And somewhat difficult to control.
Overall easier to run a rear LED, turn it on at the start of the ride and then leave it on for the duration.