Here is what I did, I was really easy and I feel you can do it to - I did this on my 66 Caravel
. First off - the old umbilical is really stiff with age. The outer sleave and inner insulation become stiff and brittle with age. Get a new umbilical with molded connector already installed from your RV supply place. Costs about $25 and will come extra long. Do not cut it untill installed - you will need the length.
I cut the connector off my old wire and pulled 2 (YES 2) small diameter nylon pull cords taped securely to the old cord. I then pulled the old wire out through the access panel under the front of the trailer. Then I used the pull cords to pull the new umbilical and brake wires through (I used one nylon line for both and saved the secound as a backup). The newer umbilical is very pliable and snaked in with no problem - I fed some on one end as I pulled. Went real easy.
You can also tape the nylon cord to the end under the trailer and pull from the front to get the old wire out.
I used a terminal strip and crimp on connectors to make my connections - the new umbilical colors will most likely not match the old wiring color scheme - CHECK FIRST. I connected all the existing wires on one side of the strip and then jumped one at a a time from the new cable until I made the right connections.