There are a lot more rodent deterrents out there these days, but before I hired a professional pest controller (mainly for termites, carpenter ants, wasps, but rodent control is included in the maintenance fee), I used mothballs scattered under the vehicles and tractor with a few left on top of the tires, which I understand is how they get into the engine bay and other areas.
During the cold weather, I keep my Mahindra 5035 in an attached garage which is heated (never goes below 45) for easy starts. It is sealed to the outside elements, which is another benefit that seems to be a good deterrent for rodent invasion as in the 11 years I've owned my tractor, I have never had any mice issues. (knock on wood!)
The detached garage seems to allow easy access to rodents... Even with the pro pest service, I still throw some mothballs under the two automobiles that are stored out there during the winter. Cheap insurance.
Of course, having to keep your tractor(s) outside is a difficult scenario and mothballs would probably not last as long in the elements (they last all winter in the detached garage)... perhaps put them in nooks and crannies inside the bodywork and frame of the tractor... just a thought.
Good luck with your repairs and the ongoing rodent control.
ng