The problem with mink oil is that while is makes a good waterproofing treatment, mink oil closes the pores of your leather, which "may" dry out your leather saddle faster. Better it just use mink oil for your shoes or boots. When it gets cold, mink oil will add/turn into a whitest haze to your leather which you have to buff out.
Buffalo Butter is a better and safer choice for break-in, conditioning, and protection with 303 Aerospace Protectant being the high tech solution and adding UV protection to prevent your leather from fading. Many Brooks owners will argue using Proofhide, but using too much of it or too often will make your Brooks sag plus Wallbike recommends treating them no more than twice a year and using a very small amount of Proofhide.
Personally I used 303 Aerospace Protectant on all my leather and vinyl (car leather/vinyl, leather/vinyl furniture, and leather/vinyl bike saddles) for years to keep them, looking and feeling like new. Lexol is the good, old standby to clean and protect leather of all types and is easier to buy locally. Quick break-in isn't high on my list, so opinions and YMMV.