Just so it's clear, Brooks specifically says NOT to use oils, look up their care and maintenance page. You will prematurely soften and stretch the leather, resulting in sagging.
Bike seats are suspended leather over a frame, they aren't a horse saddle supported by a horse, so don't use oils, neetsfoot oil etc
and sparingly use proofide if you get some.
Oh, and you'll notice on my photo that the tensioning bolt has pretty much never been tightened.