I already answered to this question in your support ticket.
However, I will paste the same answer here so that others from the community will be able to find it.
The ShowDuration property is exposed by our RadToolTipService class. It is static and this is why you cannot use implicit style which targets it to set it globally (which otherwise would be the way to set it globally). This is why with the current implementation of the service there is no way to set that property globally for all elements in one application.
Pavel R. Pavlov
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