The average plumber can repair an Eljer toilet unless it is a rare old model such as the Eljer Silette, and difficulties here would only be because the parts have been discontinued. Depending on the model, plumbers need to order specific parts online due to their limited availability.
Most toilets have their model numbers imprinted in the porcelain inside the tank. If an older Eljer toilet does not have these numbers, parts for the model can be found by searching through an Eljer toilet photo gallery or by looking at the internal parts of the toilet. Measurements of the fill valve height, tank depth, and the diameter of the valve holes are also useful in identification.