The white wire voltage should be dependent on the battery charge state. A full battery does not need charging, and the voltage on the white wire should be reduced or nonexistent if the battery voltage being sensed as too high. So, no voltage on the white wire is only a concern if the battery is depleted or if the system load is known high.
Without knowing the system conditions, I really can’t say if your measurements were truly indicative of a bad unit as received. Better luck with your next device, I hope.
Also, without knowing the internal design, it is not known whether the red wire is routed to the regulator section or only to the internal rectifier, which can be separate functions. The stock bike had two separate devices for these functions. Who knows whether the units you bought made common use of those connections. In the future, make sure the black switched power reports full battery voltage the the vreg, or it will never provide proper charging function. As you know, the black wire distribution routes through several connectors, switch and fuse contacts all known to develop resistance and voltage drops, leading to false operation of the charging system.