Commuting camera for use at night

Cycliq are best; light/camera combo, loop recording, easy to mount/remove and shift between bikes.  Used to have a Drift camera helmet mounted but it died (wasn't that old); couldn't find a decent replacement so went for a Fly 12.  GoPro best for recording fun things; they don't last long enough running continuously and you have to keep clearing the memory.

The Cycliq cameras really are terrible - it's a shame there's no company that's made a decent ride camera yet. As been said, your best bet is using  something like a GoPro sadly.

You're always going to have problems in low light with number plates.
Rearward facing cameras often have to cope with high brightness areas caused by the headlights, and this tends to make the number plate - located in-between these two bright light sources - in comparative shadow.
You're then up against dynamics as the camera will automatically adjust to cope with the lights ... Which throws the shadows even further in to darkness.
Font cameras normally have a slightly easier task, however number plates are reflecting, so shining a light directly on them will often just cause overblown highlights.
The other issue is image stabilization; most cameras will suffer from vibration in low light condition as the aperture has to be more open to let more light in, so a decent readable low light shot of a moving numberplate while on a platform that's it's self is moving and shaking is asking a lot.

I use a Fly 12 CE and a Fly 6 (first gen) and they are both pretty good on lit domestic roads, but the image stabilization on the 12 suffers on unlit country roads.
Unless you're still in blue-hour, the 6 is almost useless on unlit roads in the dark ... But then most cameras will be.

Best option I've found is to just read the numberplate out in phonetics loud enough so that the mics can pick you up.

Dont be tempted by some of the older GoPros earlier than a 5 I'd say,they struggled in overcast let alone night conditions. The 7 onwards seems to better, better than my cycliq 12 for sure, but I often think there are so many different settings, frame rates etc and then set ups with lights it's easy to end up badly configured for low light conditions, and I'm sure most people dont have the time or patience, like me,to experiment. It always surprises me no one ever reviews that aspect when they do online reviews. How does x perform in these conditions is way more important to know than how many cool mounts the camera comes with.

Hero 7 usually works if you have a reasonably bright front light aimed to catch the rear plate as they pass you too close. The problem is the failing ancient PC software, which won't allow access to the GPS data- generally it acquires it OK.

I normally run a GoPro (Hero 8) on the front and Fly6 Gen 3 on the rear, and I would say that the GoPro is significantly clearer in low light conditions. I wouldn't like to guarantee it will catch every number plate, but I think it would be you best bet. II imagine the new Hero 9 is even better. However I only got mine late last year and since I'm not commuting at the moment haven't spent too long riding in the dark with it!

If you want some sample footage, DCRainmaker has some pretty detailed reviews and videos on his website.

I was hoping someone would post here that they've got a camera that works great in the dark - maybe some of the newer crop of action cameras with HDR and optical stabilisation?

My experience with the original Fly 12 / 6 is it's quite difficult to get a clear plate at night. At least with 2 cameras and angles you get a couple of chances.

In a well lit urban area with slower moving traffic, it's pretty good. In a dark country lane with a 60mph limit, generally no chance - unless they slow down behind you before passing, then the rear often captures it.

The flashing light will help, varys the exposure for more chance. The helmet mount will hinder, as motion will cause blurring, so I'd consider mounting on the bike.