Horn blows at random MTH Railking 30204231 -What might be going on?

Sounds like possibly some random DC voltage at the switch.

Poor connections at the switch can cause glitches that look like momentary DC offsets.  Try cleaning up the track connections around the switch, my guess is the issue will be gone.

It's also possible that some locomotives are a little more sensitive to the DC offset, I occasionally get a PS/3 engine on the bench that reacts in a similar manner running on a Z-1000 transformer, but works fine in normal operation.

What would be the source of "random DC" and "offset DC"? 

If you please, define the term "offset" as used with DC.

Thank you

Tom, when there is a high resistance joint, sometimes the result ends up looking like a diode and imparts a DC offset to the AC voltage on the tracks.

If you look at the 0 in the diagram below, you'll see we have about a 10V p-p AC waveform.  The green line is a DC offset, similar to when you trigger the horn button on the transformer.  As you can see, there is now a DC component, but the AC waveform is still there.  The same effect can be observed with bad electrical connections.

I've had this issue in the past. Usually cleaning the track, running a jumper connecting the track to the adjacent track thus eliminating the high resistance, or one-time actually replacing a old switch took care of it.

Maybe a case of substandard employee performance. Have your engineers been checked for drugs recently?