Further to my earlier post, I can confirm brightness can be controlled by turning the display's internal power on and off. Specifically, the command $FE, $13 uses the "Cursor/Display Shift/Mode/Power" command to turn off the internal power and dims the display, and the command $FE, $17 turns on the internal power and sets maximum brightness. Once either command is sent, there is no effect on existing brightness until a subsequent character write occurs and changes the brightness of the entire display.
However, there is nothing in the WS0010 spec sheet that specifically states that the purpose of turning internal power on and off is to provide brightness control, and there is not any brightness gradient control that I'm currently aware of. I've not yet checked to see if internal power on/off can serve as a reset command for the display. Turning off internal power (whatever that really means) might just result in powering the display parasitically from the signal inputs, and if this the case, it can't be beneficial to the display's health in the long term.