Ok so you bought LED lights that were already ready for hookup ... good
It sounds you had a short in the line, the positive and negative wires are touching each other with no load to power, ummm ... I'd say it was probably the LEDs you got. If everything was fine before this happened then you probably got defective product.
If you can rewire your Neons to double-check and make sure everything works on that switch.
Also did you originally have that circuit fused ??? because causing a dead short, should have blown a fuse unless you were taking power directly from the battery. Which isn't a very good idea.