I also have a 2007 Edge and no air brakes on the Alpine.
Having towed the edge over 16K miles using an Even-Brake and Aventa tow bar on the Edge base-plate, we have experienced no problems.
However, as the Alpine has red stop and amber signal lights, I chose to not tap into the Edge brake light system and installed an auxiliary light bar between the Edge's roof rails and school bus size LED lights aside the rear license plate.
Additionally, I installed a "Toad-Charge" powered directly from the Alpine's chassis battery through the 6-pin connector.
We have been very happy with the set-up and never move the Alpine/Edge combination without 1st installing the Even-Brake.
If I can help with any further information, please feel free to ask.