It's not the easiest to find a rear light that's usb rechargeable - I'm not sure why.

Finding one that has a rack mount, even harder.

Having the light screw onto your rack is a good idea, that's what I do. I've also had a bit of similar frustration - I'd like to leave my rear light plugged into a charger, so I can always be 100% sure it's always charged when I head out riding. The Cygolot looked to bright and annoying (my ideal would be the Planet Bike rack blinky), this one looked interesting -

MetroFlash Nocturna USB Rechargeable Taillight with USB Cable
Amazon.com: MetroFlash Nocturna USB Rechargeable Taillight with USB Cable: Sports & Outdoors

But it looks like it's attached with a wraparound thing, so might not work with a rack or rear bag. Grr.

My best solution so far is to buy enough rechargeable batteries that I just swap the batteries in the light with a freshly charged pair, so it's not to inconvenient, but it would be nicer to just be able to plug a cord into the light every night.