What about powering off the whole thing, disconnect it from the power. Apply power back to it, hold down the VREN button for the 5-6 seconds to turn it on and then check it with the phone/computer? Seems odd there's some mystical way to get it to get into pairing mode.
Failing that, I wonder if the support circuitry in the WideHK docs has to be used to perform some initial magic on it at power up, or setting some internal modes.
The one LED seems to just indicate that power is on (they talk about showing charging a battery and using it as the indicator), whereas the other one seems to be for the BT connection itself. But I scanned the docs and didn't see anything about any flashing rates for paired or non-paired.
I've done a lot of work with standard Bluetooth (HC-05's) but never ventured into BT audio.
Judging from some of the other bluetooth audio modules on fleaBay, seems that a good number of them come on breakout shields so you can utilize them easier from the Arduino. That's why I thinking there's some more circuitry required instead of just power.