Welcome to the forum!
There is much that needs to be checked to get these postwar horns to work properly.
First, familiarize yourself with the parts of the horn and its circuit here.
http://pictures.olsenstoy.com/cd/locos/loc2023b.pdfMake sure all the parts are there and the wiring is good and intact.
Look over ALL the parts, and insure NONE have any corrosion on them. We are dealing with 1 1/2 volts DC here, and the circuit must be pristine for it to work.
Here is the schematic of an engine with a horn circuit.
http://pictures.olsenstoy.com/cd/locos/loc2023a.pdfAfter all the parts are clean, you can check out the horn and its circuit.
First thing to do is take a fresh battery and touch the bottom end of it directly to the horn casing. Take a jumper wire and connect the top of the battery to the horn wire where it is connected on the relay. The horn should blow loud. If it does not blow, the horn is bad.
Next, put the battery in the engine and close the bottom battery plate and tighten it.
Now lift up the bottom of the relay by hand so that the points make contact. The horn should blow. If it does not, the relay contacts may be dirty/corroded and need cleaning and burnishing with a very fine emery board. The horn needs to work properly at this stage.
Next in line is to check that the relay is closing under power. Put a few lighted cars on the track, turn on the power, and get the engine in neutral and lock it there using the 'E' unit. Now try the transformer whistle control. You should hear/see the relay close, and the horn should blow. If the relay does not close under power, the transformer may have a bad whistle rectifier and it will need to be replaced.
Do these diagnostics in sequence until you find out what your problem is.
Larry