Warning: Wayward philosophical-aesthetic ramblings ahead!
When I've pondered the meaning of the phrase "a painter's painter" before, I've pretty much decided that it describes an artist whose work appeals strongly to other painters, often moreso than it appeals to other audiences. Other painters admire the paintings such artists make for their daring and original answers to the myriad "problems" of painting that every painter encounters over the course of learning the craft.
Such a painter often revels in the material qualities and what painters call the "behavior" of the medium itself. They don't make "likable" pictures in the sense of basing their works on what artists of the past have discovered people like (and will therefore buy). They purposely put themselves beyond the reach of conventional representation and technique.
Painters' painters therefore have an evident authenticity or honesty in their work - they're going on instinct and originality and it shows. They embody what all oil painters feel to some degree in the adventure of painting. By doing so their work ends up to some extent being about painting.
Such paintings, by their striking presence, literally embody the act of making art. When we encounter their paintings, instead of admiring the technique or interacting with the content alone, we feel the artwork as a reference to, and often a celebration of, art-making. I think painters send in it a signpost toward their own honesty and call to creative self-expression. Any work made this way, artwork with presence, feels fresh, honest, and celebratory and seems to me to exemplify the role of the artist as explorer of human existence.
Some hallmark of "painters' painters" works I've loved:
Thick applications of paint (known by the Italian term "impasto") emphasize visible and expressive brushwork. Painting mediums like thickened linseed oil (stand oil) enhance the inherent buttery "juiciness" of oils.
The enjoyment of an experimental unfettered spirit prove the limits of all those pesky concerns with accuracy and rule-following.
Original (non-cliched) compositions avoid established harmonious design principles in favor of newly invented, intriguing geometries. Subject matter departs from the traditionally admired motifs of the history of painting (with which said history, and technique for that matter, the painter must be thoroughly acquainted in order to deliberately avoid repeating things already been done by someone else).
The best "painterly paintings" (something by Rembrandt, Monet, Bonnard, Jennie Saville, Cecily Brown or Lois Dodd, for example) exude a fascination with the puzzle of art-making in general (why and how it's always been done).
It seems to me all great art has some aspect of this presence about it. (An aside: As a yardstick to test a given theory of art, I often apply it to a trio of greats and see how well it stands up for all three: usually it's the cave paintings of Lascaux, Michelangelo's David and Sistine Chapel or Rembrandt's self-portraits, and either Monet's Water Lilies or Jackson Pollock's "Autumn Rhythm." In this case, I think any of these works can be said to have a great degree of presence partly due to the artist's handling of the material).
But even all of that is still just technique. Presence comes from something other than the surface aspects of "painterly painting," such as visible brushstrokes, drips and marks. A painting, to be more than a visual delight, has to have content. "Content" is a squishy word in art, but it's one we must use when we want to point to what sense the artist has put into the work - the complicated amalgam of specific emotions and ideas that elevate a work above mere representation or decoration.
Bonnard is a painterly painter who also has content (his opulently painted, luminous domestic scenes and interiors reveal the splendor of the everyday). Jenny Saville has content (her nudes wrench back a raw, suppressed reality from hundreds of years of oppressive idealization of femininity). However, this idea sometimes gets expressed as the dictum that paintings have to be "about" something, and plenty of artists find this idea irksome, and for good reason.
Many artists detest the notion that their work has to "make a statement" for two reasons: 1. because of their personal devotion and love of the visual (as opposed to discursive) qualities of the medium and 2. their correct their sense that art comes from a wordless, mysterious, place that has nothing to do with "statements" about anything. They rightly sense that the strongest art should not, and indeed cannot, be reduced to a single meaning or message. But that doesn't mean it means nothing or has no content, does it?
I suggest that a serious problem with such reductionist attempts to pigeonhole art is precisely the failure to recognize presence - inherent in which is the unbreakable marriage of form and content - the union on the one hand of meaning, not in the form of a literal "this means that" formulation but in the form of evocation (something that triggers memory and association of ideas and experiences), and on the other hand, the glorious physical qualities of the medium itself.