Strike my previous post about leaving the Black wire disconnected. I found some different instructions from BRK. Looks like Black/HOT is used to power the relay.
EDIT : Ok so now BRK is giving conflicting information. It may still be possible that Black/Hot is a pass through for power. Still I would do what I recommend below and add an extra Test with the Meter. Once the relay has fired you need to test if you are getting 120VAC through either the Blue or Gray wire. If you get 120VAC through either of these then you may want to disconnect the 120VAC Black/HOT.
Personally I would test it this way.
Hook up Black to HOT, White to NETURAL and then Orange to NEUTRAL.
Get a Meter and test continuity between Brown and Blue. If you get continuity then the Relay has fired. If you don’t it hasn’t.
If it hasn’t then try putting Orange to HOT and test continuity between Brown and Blue.
NOTE: I would put the Orange wire to Neutral first to test. This way you won’t accidentally blow out the relay. If going to Neutral activates the Relay then you know it was meant to go to Neutral and not to BLACK/HOT. If it doesn’t fire the relay then you can be pretty certain it needs HOT power.