If the red light is on, it is charging. If the red light is not on it is not charging. If you plug your reader into a USB wall charger, I don't think the red light will come on. If it does, it will probably only be on for a few moments and then it will go out.
I haven't tried a USB wall charger myself, but I've read quite a few posts here from people who have and it didn't work for them. What I have done personally is have my Reader plugged into my computer and used the eject button within the Sony software. I did not immediately disconnect my Reader from the computer. The red charging light did go out, but I just figured it wasn't charging or discharging at the time.--Wrong. By leaving it plugged into my computer after ejecting, the battery meter dropped two bars in a couple hours! Lesson learned! Always physically disconnect the reader after "ejecting" it in the software!
dordale