I've only played the Fender Player mustang, not the HB.
The stock wiring was not ideal as a '50s style' circuit was used which reduces volume when rolling off the tone unless the volume is set at 100%.
I made a new loom with better components and more sensible circuit for mine, and shielded the cavities with anti-slug tape. It is a great little bass now, and the stock pickups sound excellent.
I don't know whether the same circuit is used on the Player II (with the 'spaghetti' logo).