Hello. As you probably know, the word amaeru is derived from 'amai' which is ofcourse 'sweet'. Amaeru would be the active form and 'amaya-kasu' would be behaviour that allows 'amae'
How about some of these definitions:
Amaya-kasu : over-indulge, coddle, be too lenient, pamper, spoil, be soft on.
Amaeru: (when work related) expecting leniency, indulgence, forgiveness for ones's blunders etc. (on a more personal basis) to be a baby (sometimes in a nice way), behave like a spoiled child.
The more I think about it, this is a tough one....Anyway, hope that helps.

As a shakuhachi musician and as someone who had read Takeo Doi and worked in the field of psychology, I feel the need to enter an alternate explanation of amae and amaeru. First, let me say that I do not disagree with the present posts in terms of social-psychology. But there is a much deeper, more creative meaning that in some ways is equivalent to the English words " to intuitively understand" or the popular English phrase "to be in sync" or , even more, Robert Heinlein's science fiction word "grok" (from his book "Stranger in a Strange Land"). If one deconstructs the common word "understand", one sees that this word has a very strong relationship meaning that implies physical support, holding and providing a firm foundation. An interesting comparison with amaeru is with English child psychologist DW Winnicott's use of the terms "holding" and "facilitating environment" in describing the early mother-child relationship.
For a musician, this is the essence of what makes a band "swing" or "enter a groove" or not. The band members create a "facilitating environment" for each other, such that the creative whole becomes greater than the sum of the skills.

In both cases, mother-child and band, there is a mutual dependency on each other for one's individual fulfillment, along with a deep gratitude for such intuitive "knowing". In terms of the other references to journeymen in bars with young women, it is as if the men are saying :"You know I am better than what I seem. There is more to my 'soul' than my role in society suggests." It is this sense of sharing knowledge of a "greater wholeness" that amaeru seeks to express.

In the most ancient Japanese shakuhachi (bamboo flute) tradition, the music ("honkyoku") of the wandering monks ("komuso") of the oldest Meian-ji "sui-zen" tradition ("blowing meditation"), the ebb and flow of the rich "soft-edged" sounds of the bamboo flute (as contrasted with the "hard-edged" sounds of metal instruments) and the bending tonalities (think of a great slow blues guitar musician like Buddy Guy for an easy definition of "bending tonality") , along with the lack of a melodic line, creates just such a "facilitating environment" in which one is "awake" and aware, but not "taken" anywhere.

In sum, Amaeru is an expression of such a seemless, intuitive compatibllity and coherence, as expressed both in the mother-child dyad and the "creative space" of an artist.