Do not think you will ever regret electric trailer brakes, I am so glad we have them but you may need a battery and breakaway switch then.
In Ontario the MTO rules make it so we can not pull our trailer without brakes as the trailer weight is over 50% of the car weight. The car is just over 2700 so 1400 or more we needed brakes. We also needed the breakaway switch as that is law in Ontario with electric brakes.
Brakaway switch was only $17 but the battery may hurt if you do not have one; most 13' units have a battery.
Dealer recommended the transaxle cooler and our Corolla came new with brake module and a hitch installed when we purchased the car along with all of the available optional safety systems. The last trip was only 1 1/2 hours; mostly up hill and the car did it fine no change in temp guage. The return trip will be mostly down hill so again glad we have brakes.
Hope your summer was as good as ours.