The problem is that you have to start considering the failure modes of the failure detection system. You're quite likely to end up with a less robust system or a lot of false alarms if you have a system designed to warn you of failure.
You also have to consider what faults would be detected:
- a dead battery? You'd need another power source to feed your warning
- a briefly open contact causing the light to switch off (I've had a proper brand light do this every pothole on a road bike)? Can this be distinguished from a deliberate switching off?
- accidental switching (e.g. bumped by a pannier)? How is that different from switching it off?
- unlikely failure modes like LED burnout? These shouldn't happen in a well-designed system, and I wouldn't trust failure detection in any other system.
- the light falling off? Quite a likely failure mode but an extra fixing would be more reliable and less effort - and your failure warning service could fall off too.
- Damage (which could be things like a failed connection or loss of focussing optics) due to vibration/fatigue/impact. My helmet-mounted rear light has lost an LED to this, and another flickers, so it happens. With series-connected LEDs (common on e-bike rear lights) or a failure in a common electrical path, you could easily lose the whole output.
So instead we consider a system designed to confirm that the light is on. If the confirmation fails you stop and check. This could be a design or mounting that deliberately directs a little of the light to where you can see it. Simply mounting your rear light on your seat tube and having a silver-coloured pannier rack is an easy solution to this. A light with some front-facing white/yellow lights that shine between your legs would cost battery power but might increase visibility.
There are big advantages to multiple independent lights:
- you're more visible from more angles (and further away if you add lights up high)
- approaching vehicles can get an idea of how fast they're gaining on you (this really needs multiple constant lights to work well)
- they indicate your size better - important if you're wider than a driver might expect (trailer for example)
- and of course the big one here: if one dies you've still got some minimum level of lighting at the back.
I take this approach with two steady rear lights and a flashing one on my helmet (also with yellow LEDs on the sides). Sometimes I have a third rear light as I have one on the top of my daughter's seat and one on my spare pannier.
Another consideration is what you'd do if you detected a failure and it wasn't easy to fix at the side of the road, an hour from home, in complete darkness. With a backup light or two, just ride on. Of course this does mean you should check your lights at home - this is just a matter of looking at them as you switch them off and not doing it by feel.