I have a winner on the inexpensive front. I use a rear blinky every day and got tired of throwing out lights when the intergrated battery died. So for me, using AAA rechargables was a criterion. This
Aliexpress gem is great. It's cheap, the bracket is nothing special but works okay. You'll need to swap batteries every 10 hours or so; unlike lights with Li polymer batteries, this one will slowly lose intensity but keep running. I'm several months into daily use (through the winter) and it's been perfect. And $3. I have 3 because why not.
Will