I presume you mean, for no. 1, that unlit cyclists involved in accidents are even rarer than unlit cyclists on the road?
Not really. I'm not commenting in any absolute sense on how common either might be. What I am saying is that statistics that show that unlit cyclists in accidents are relatively uncommon pose a problem for anyone who claims that unlit cyclists in general are very common.
Say the statistics show that 1 in 5 cyclists involved in an accident (at night) is unlit. If you claim that unlit cyclists are twice as likely to be involved in accidents, then only about 1 in 10 cyclists can be unlit. If you claim it's ten times more, then only 1 in 50 cyclists can be unlit. If you claim that 50% of all cyclists at night are unlit, and lack of lights makes you ten times more likely to be in an accident, then you'd expect something more than 90% of all the cyclists in accidents at night to be unlit. But my recollection is indeed of something like 1 in 5 casualties being unlit (in the statistics that I saw years ago). That simply doesn't allow us to maintain both ideas (that the proportion of unlit cyclists is high, and that the risks of not having lights are high), at the same time.
Note that, for this purpose, "cyclists" means "cyclists you see out and about", which effectively means that those doing more mileage are more likely to be counted.
...but also because drivers tend to take more care around unlit cyclists.
Precisely. One of the arguments advanced to explain the apparent discrepancy between the claims is that unlit cyclists, generally speaking,
are seen, and annoy drivers so much that they grab attention. Otherwise "I saw a cyclist with no lights today..." makes no sense
Whereas lit cyclists suffer from the much-discussed effect under which other road users see them, subconsciously assess them as not a threat, and move on to assessing the next risk.
Please, for the avoidance of doubt, I am not arguing for riding without lights, not least because I don't have confidence that the above, unreferenced, statistics are sufficiently rigorous, or supported by other studies, to stake anything on them, let alone my life. I do, however, see them as supporting my general contention that perception is much more complex than the "dress up like a Christmas tree" visibility arms race argument allows.