I don't recognize the controller, which honestly is not shocking, but I would rather assume you have one power wire, and a ground wire.
if you are saying that the connector to your light has a different connector, I would reccomend checking the black and yellow wire off the controller with a multi-meter, figure out which is power, and which is ground.
Look at the diagram for your light if you have one, if not *IF IT IS AN LED* it will probably only work if the power is applied to the right wire, so, feed power and ground into your connector, figure out which one is which on your connector.
Then, you have a few optional approaches:
You can rewire either the controller or the lamp to match the other side
or
you can make an adapter cable that has the correct plugs on either side and plug it in between the existing wires.
This is basic wiring issues and from what I have gathered, is the bread and butter of DIY in ebikes. My answer was to purchase a kit that I liked the sounds of (and had referrals) and then figure out what I am going to use as connectors for my build.
I am not going to go with whatever is in place from 3 different companies, I am going to build my custom bike with wiring that makes me the most comfortable, if I have to change every tip on the unit I am ok with this. I am one I guess extreme of preference. There are others. You need to figure out which way you want to go with it.
