How to describe this

They mostly have stacks of books laid out, with the artist drooping rather plaintively behind them.

We've been around on this one several times. Here's how it breaks down:

Robert: "Drooping plaintively" evokes a sense of pleading (for customers), along with helplessness.

Laura: "Drooping wistfully" better conveys yearning tinged with melancholy (over the lack of customers)

Our friend (and Robert's editor) Elizabeth: "Drooping languidly"--lacking in vim or energy or
"drooping torpidly"--having lost motion or the power of exertion or feeling, sluggish in functioning or acting.

Neither of the ones I like have that beseeching quality you're looking for, but they add to the general tone of ennui you're evoking.

So far, we've invested a rather impressive amount of brain power into choosing one word.