Incumbency

I recently came across a not-new word, used in a new (to me) way. The word is incumbency, used to mean a personal obligation. In a 1966 Nero Wolfe story, Death of a Doxy*, Wolfe explains his interest in trying to clear an accused man by saying:

Mr. Cather has worked for me, on occasion, for years, and I am under an incumbency. 

It took me a few moments to figure this out, though I'm familiar with the more common form, “It is incumbent upon me ...”

* Doxy is a term I've never heard used, so it must already have been out of date, at least among younger people, by 1966.