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Mine had the same problem. I ended up just replacing it and was happy with the results. I tried mink oil and leather conditioner with little success. I think I paid $40 for the replacement.
as long as there is no cracking in the leather, there are several products that are supposed bring dead, stiff, leather back to life. leather honey, and leatherique rejuvenator oil. both products are fairly thick with the consistency of STP. basically, a heavy coat, and let is soak in over a couple days. I've had limited success with both. the problem I see here is the stuff probably cost more than a new, replacement shifter boot.