Here's an example of confusing elegant variation:
Born in Woodmere, Long Island , on May 22, 1930, Milk was the younger of two boys in a family descended from Lithuanian Jews on both sides. (Their last name was originally Milch.) Milk's paternal grandfather maintained strong ties to the synagogue he helped build in his grandson's hometown.
(Als, Revolutionary Road (March 12, 2009) The New York Review of Books at p. 8.)
Take a few seconds correcting the final sentence to eliminate elegant variation.
If you assume avoiding elegant variation means repeating proximate words, you substituted "Milk's" for "his grandson's." The cure, here, is worse than the disease: surfeit of Milk gags the reader. The writer gains Concision and avoids both elegant variation and cacophony by substituting "Woodmere" for "his grandson's hometown."