From what I have seen and go by, the breakaway is to be hot all the time to the camper battery. If you have a battery disconnect, it goes on the upstream side of the switch so you always have the emerg back up power available.
As to a fuse for short protection, mine does not have any on the breakaway. That said, if you want one, I would go with a self resetting circuit breaker over the fuse. I would pick a 30 amp, I have no 10# awg brake wire except for the break away. A dead short should trip it fast enough before total melt down. In my case the , #14 gage wire on the breakaway switch becomes the fuse.
To your question on a resistor in the break away switch, I have not found there is one in the switch. However the setup can create a voltage drop. Most have 6 feet of total wire length, 3 ft to and 3ft from, the switch. That #14awg may be your voltage drop point. And the switch itself may have some resistance drop. I noticed the same thing on my sons PU. While it is live hot to the battery, that does not mean you will deliver full current to the brake coils. Poor trailer wiring and then the smaller gage wire at the switch does not help the cause.
Hope this helps
John
2005 Ford F350 Super Duty, 4x4; 6.8L V10 with 4.10 RA, 21,000 GCWR, 11,000 GVWR, upgraded 2 1/2" Towbeast Receiver. Hitched with a 1,700# Reese HP WD, HP Dual Cam to a 2004 Sunline Solaris T310R travel trailer.