For any trailer, you'll of course have running lights, right turn/brake, left turn/brake, and ground. If your trailer has brakes (my 16x7 enclosed trailer does), then you'll also have a wire for that. The standard trailer wiring colors are:
Brown=Running
Green=Right turn/brake
Yellow=Left turn/brake
White=ground
Blue=electric brakes
Red=battery/aux (this would typically be used for interior lighting)
Purple=back-up lights
Use a continuity tester and see which terminal (on the trailer plug) corresponds with each wire in your "box". Standard trailer plug layout diagrams can be found at etrailer.com
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2004 Itasca Sunrise M-30W
Carson enclosed ATV Trailer
-'85 ATC250R, '12 Husky TE310, '20 CanAm X3 X rs Turbo RR
Zieman Jetski Trailer
-'96 GTi, '96 Waveblaster II