Blue wire in the umbilical cord and under trailer wiring is typically the electric brakes. The breakaway switch connects between the blue wire and the positive side of the battery. Do you have a VOM (Volt/OHM meter)? Even a 12 volt
test light would be good for the first check. Check the two wires for voltage. If one of them has 12 VDC, that wire probably comes from the battery. You can make sure it does using the OHM meter function to check for continuity between that wire and the positive terminal wire on the battery. To be totally safe and not cause any sparks, disconnect the battery before checking for continuity. A zero OHM reading, or close to zero is what you want to see.
Now use the OHM meter to check for continuity between the other blue wire and brake pin on the umbilical cord. See below for where to find a diagram. If it's also zero or close to zero OHMs, then that blue wire is connected to the umbilical cord, and therefore the brakes (assuming that your electric brakes work while connected to the tow vehicle).
If both of those checks are good, then yes, the two wires on the breakaway switch connect to the blue wires. One breakaway switch wire connects to one of the blue wires, and the other breakaway switch wire connects to the other blue wire. Doesn't matter which switch wire connects to which blue wire.
Reconnect the battery, and you're all set. Pull the pin out of the breakaway switch and it'll activate the electric brakes. But, don't leave it out too long as it applies full battery voltage and current to the brakes.
If neither blue wire has 12 VDC, there may be a fuse that has blown. That might take a bit of tracing the wires physically to see where they go.
Here's a good reference for umbilical wiring:
Scroll down to find the 7 PIN RV connector you have on your trailer.