You should keep the topic in one thread so all info is one place, folks don't have to ask about things again and again.
The horn needs dc from a bat., a whistle relay only closes points between batt, and horn, like a switch.
So is the relay chattering on/off/on or is the horn not getting good battery power thru the points? Clean and sand/file between the points where the touch when closed.... lightly, straight, flat, level... they should be flat&smooth and touch level when closed. Little tits can build up on points over time as jumping electrons(etc) drag a few metal molecules across the air gap(s).
The Lionel whistle relay is a slug relay. A very special relay that operates on DC, but not AC. I doubt you will find an equivalent relay. Usually the problem with horns is there are just too many contact points in the battery circuit, which is only 1.5 volts. As Adriatic said above, clean the contacts on the relay. Another problem is the relay armature hinge point. Many people add a super flex wire shunt around this hinge. Find as many of the other contact points as you can and dissemble them, clean them, and reassemble using a little silver grease. For those contact points you can not get apart, try spraying a little Deoxit D5 on the joint.
It isn't hard to swap a relay. Hijacking is when you post off topic" taking over" or draw badly away from the OPs ability to solve their issue. Reviving old topics for continuing it isn't a highjack if on topic.
Starting a new topic is no sin sure.... fyi, I thought from the wording you had already posted about this. Not enough info here to make it easy on anyone trying to help.
.....Or I might know, or others too. and no a pc's dc relay won't be able.to tell ac from dc. Nor any trick to. The closest thing was old telephone relays(where lionel got the shunt relay originally) Knowing how to address most issues and recalling exactly what's there aren't the same thing all the time
Solder the relay post.... loosing a connection at an old rivet can sometimes be fixed by solder, yes. This applies quite often actually, so backtrack along the battery traces/rivets/connections too.
Voltage crosses bad connects easily until the amp draw rises, then the volts may drop fast where there is some resistance to amps. Testing volts while the horn sounds (loaded); test at the horn terminals too.
You aren't looping any wires near the relay coil are you?
edit: auto.composer added an extra "voltage" after amps...now removed
@David Johnston is correct in that the Lionel Relay is extremely specialized and not something you will find an off the shelf electrical replacement (not evening going to think about physical form factor here) for from Mouser, DigiKey, China, etc....
However, there are circuits you can build yourself to replace the relay:
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