Installing trailer light connector, and it doesn't fit

So my truck didn't have a tow package, not even a receiver.. so I bought a curt receiver, and a Reese light connector for trailer lights,. However, the connector is too long to put in a logical location, I.e. at the edge of the plastic before the steel part of the bumper. If I place the connector there, it runs into the receiver. Any suggestions or experience relocating in an easy location?