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Part of the answer may be to tune-up the transformer. In addition to cleaning the contacts throughout the horn circuitry, including the "ground" side, I installed new diodes a la the method clearly explained by Jim Barrett some years ago, using precisely the parts he recommended. Have also repaired and in one instance replaced the horn itself. Result: the replacement horn works reliably but doesn't sound like the old one; and the repair was moderately successful at best.
Next I ried a "SuperHorn" by Depotronics, as I recall. It worked well, but I don't think they are available any longer. There are other electronic systems on the current market, however, and one of them might work for you; but if it has to be 100% original you will may have to try to find "new, old stock" horn or maybe one from a junker. Upgrade any postwar ZW or KW as suggested. Similar mods can be made on other postwar transformers, but perhaps not quite as easily.
The mechanical horn/whistle relays in the locomotive may well need attention but you have to be extremely careful not to do more harm than good. Gently cleaning the contacts and/or placing a tiny layer or two of tape to prevent the relay armature from "stcking" may help if the horn doesn't shut down reliably, or replace the relay if you can find a good one. Check the mechanical operation of the relay. Sometimes the springy portions get bent. Cleanliness is a whole lot better than "gunkiness" where relays or "steppers" (such as electro-mechanical E-units) are concerned.
I wish that Lionel would have put digitally mastered Lionel Postwar Diesel horn sounds in their CC series.
Alan
I have a 2350 Hew Haven EP5, and the horn hadn't worked in nearly 50 years. Last year, I did the following fix, and it has performed flawlessly ever since.