The relay most likely only 4 leads to it, correct?
Should be (I'll use numbers from a standard Bosch style relay - the numbers may be on your relay as well, they are standards):
- 30 - Constant power in (could be key-switched power unless you want the lights to be able to be on with the bike off). This is the main power that'll feed to the lights, so you do need to have some concern with the current draw on this circuit, if you are tapping a fused circuit.
- 86 - Switched power in. Probably a switch that came with the lights, or you could tap voltage at the wire going into the headlight if you want them on all the time without an independent switch.
- 85 - Ground. This is just for the magnetic switch inside the relay, but it doesn't work if you aren't grounded.
- 87 - Supply power out. This powers your lights.
If it has five terminals (standard Bosch style relay), then there's an additional terminal that becomes engaged when power is removed
from the circuit - labeled 87a. You do NOT want to use this one.
From your complaint - my first guess would be that you are using that one.
In that event, when you turn the switch in the direction that supplies energy to the relay, the lights would turn off, rather than on - and with the switch in the position that you are thinking is "off", you're creating a drain on the battery.
If you use terminal 87 on the relay, then when the switch is truly "off", power is cut to the relay, the connectivity to terminal 87 is terminated (87a becomes engaged simply because that's it's fall-back position), and the lights will go off.
My guess is that possibly they gave you a real 5-terminal relay, with instructions to not use one of the terminals, and you are simply plugged into the wrong one, from your symptoms. 87, not 87a.
Let me know if I'm right.