The RE wiring diagram also says amber is the common leg (-).
https://accessories.hitchcocksmotorcycles.com/core/media/media.nlid=238415&c=1062795&h=733dc903b88af9a659b4&_xt=.pdfWith the key off, there should be about zero ohms between amber and battery negative. If there isn't, find & mark the wire that does. Find & mark Hi and Lo, they are (+) when selected by the hi/lo switch with key on.
The LED works as its factory schematic says it does. Check their website and verify their connection. Now you test the LED to verify it really works. Connect up the LED to a 12 V battery as per the manufacturers polarity to energize HI, then connect again for LO.
A this point you have a working LED "bulb", and you have also ID'd the wiring from the bike,
regardless of color code, that actually performs the desired function.
If you now connect the bulb in the circuit using the manufacturers connections and bike wiring you have sussed out, it has to work. Likely if the wire color code isn't right, it either got miswired or the assembly line folks got creative on Friday afternoon.
Good hunting - ACR -