The first iteration of this project worked quite well. However, it wasn't very compact because the blinking was done by an external Arduino board which was overkill, messy, and needed a separate power supply. So for the second iteration of this project, I decided to make the control circuitry contained entirely within the UPS.
Step 1: Make a blinker circuit. It turns out this is really easy to do with a simple 555 timer IC and some help online. I picked my resistors and capacitors to give this a duty cycle similar to other bike lights I owned. This is a picture of the circuit on a breadboard before I soldered it up to protoboard that shows how simple it is.
Step 2: Find power in the UPS. It didn't make any sense to power this thing externally when I was dealing with uninterruptible power supply with plenty of control circuity. The 555 timer I bought works with anywhere between 4.5V and 16V. So I turned the thing on and carefully probed measured various places on the board until I found one that was giving me 12 volts. After that, getting the electronics working was as simple as soldering it all together.
Step 3: Put it back together. Finally I was ready to make it look pretty. I taped up wires, put the 555 circuit in some extra space, and added a couple a couple doses of hot glue. Afterwards you wouldn't suspect that I had been in there are all. Success!
I did actually use this on a few rides to and from work and it worked splendidly if a bit heavy because of the lead acid battery. Especially at night, the traffic light is amazingly bright. A great next step would be ripping out all of the AC circuity and getting this working with some lighter batteries DC only.
Technologies: A/C Electronics, Basic Electronics, soldering iron