If your tractor sets out, water more than likely get in around the shift levers when it rains, even if they have boots on them.
A good mix to clean is a 50/50 mix of ATF and diesel, plus 1 quart of rubbing alcohol. Filling to 2/3 capacity will probably be enough. ATF is a high detergent oil that will clean things up inside, diesel will wash it down, and the alcohol will absorb any remaining moisture left in there.
Drain transmission and refill with mix. Drive around for 10 minutes or so to let it clean things up then immediately drain. Might pour an extra gallon of diesel through for a final washout. Then refill with proper fluid.
This is a picture of inside the differential/transmission of my little Farmall 140 that the oil looked like a yellow milkshake when I drained it. You can see how well it worked to clean it up. Debris in the bottom is from a bearing on the PTO I had to replace, mopped that out with a shop rag.
I first used this mix 15 or so years ago to clean up the trans./differential on an old Case backhoe and the results were the same. Pricier to do now than it was for the old backhoe as it held 5 gallons, and the little Farmall only holds a gallon, but well worth it to me.
If your tractor sets outside, cover the shifters with a small tarp, or even a 5 gallon bucket upside down, anything to keep rainwater from running down the shifters into the transmission.