Thank you for the picture, Mike.
It is possible that your locomotives may have been assembled from spare shells and chassis by a dealer long ago. Dealers were known to make custom trains from spare parts, so occasionally a train is seen that does not appear in any listing, and does not match any known factory variations. It is possible Lionel may have made the locomotive at their factory from spare parts also.
Without knowing the history of the locomotive and its' original owner, one can only speculate.

The 2343, 2344, and 2345 all used the same chassis and shells.

The service manual for these engines is here.
http://pictures.olsenstoy.com/2355p.htm

To check the horn, take a fresh battery and touch the bottom of it to the horn itself. Take a length of wire and touch the top of the battery to the horn wire on the relay. The horn should blow. If it does, the relay battery contacts and frame need to be cleaned of any dirt or corrosion.

Larry