Surfing e-Bay, I found item number 280346932197, priced at $32 with the following description:

Replace your lost adapter from your original trailer lighting kit! This adapter is identical to the one manufactured by Land Rover. The large plug is for the standard European 12N 7 Pin trailer light and the 4 pin flat connector is the standard for US trailers.

Note you must have the European socket as shown in the second picture mounted above your hitch. This adapter does not connect to the socket behind the right hand tail lamp assy.

This product is made from new products by Siouxland Rover in the USA.

 

Still need to add a power lead to that to allow it to run any trailer lights.

 

The Euro version has two sockets, one for the trailer and one for trailer accessories, like a refigerator.
What you are describing sounds like the Euro 7/4 adapter. Plugs into the Euro 7 pin trailer socket to convert to 4 pin. Do not know if would work in US, think are wired differently.

J.C. Whitney use to carry them, but don't see on their site now. A Google search shows the Pollak 7 to 4 pin adapter for $ 6.95. Can't tell if for round or flat pin, but pricing should be similar. Here: http://www.heartlandlock.com/index.p...0efd9de55f77cb

 

Sweet! The Heartland link also has the 7-to-5 adapter that someone was looking for recently to hook up his surge brakes.

Needing the whole wiring setup for mine, I went with the Atlantic British kit, which terminates in a flat-four. I only do light-duty towing, and that's completely adequate.