> The only things I didn't add were the battery clip and the LED.
No, you "added" a wire-path where the LED-and-resistor are supposed to go.
Say I have 120V power, a switch, and a motor. Well, say I don't have the motor yet. So I connect the switch then put a wire in place of the motor. When I flip the switch, HMMMMMM!!, fuses pop, and then the lights go dark.
The critical thing you need is SOME non-zero resistance in that area. A 1K resistor will pass at-most 9V/1K= 9mA, which is a strain a battery can stand and a wall-wart hardly notices. Just like that, it's just waste power. However that 9mA is ample to light an LED, which is what that path was *supposed* to be for.
You NEED the resistor. Just-a-LED is not enough. The LED will conduct "infinite" current if you apply more than a few volts and do not have that Current Limiting Resistor in series.
General tip: if you don't have a part, don't replace it with a wire. Sometimes it is no harm, sometimes it "works", sometimes that's even a good substitute. However if you don't know, you risk burning the wires.
Minor point: the drawing you base-on shows flat terminals oriented horizontally. Your rendition, I can't tell. In a 2x3-terminal switch, we can figure it out. But on the 3x3 switches, there are two ways to wire 3x3 terminals and one of them is very wrong. (Maybe you got this and didn't need to draw it for yourself.)
> I hear a "tick tick tick" sound.
It sometimes helps to say what you use for power.
Battery and linear-warts don't "tick". But a Switching Supply, faced with a fuse-popping short, will usually shut-down start-up shut-down start-up a few times a second to protect itself. "tick tick tick".