I don't recall just when AS changed from the double plug umbilical cord back to the single one. Many '70's AS had the double plug system. I think your '77 has the double plug system.
If you have a socket on the front of the trailer for the umbilical cord to plug into the common Bargman type flat blade plug with molded cord can be used for the truck end, but the trailer end will have to be wired with the round blade Signal Stat type plug. Realize also that the color codes have changed from those years of AS and you will need to get the original color code chart vs. the newer one used today. I don't have a reference to the old vs. the new color codes, but someone here does and can post them please.