King America Harley Davidson Lamp does not work.

$75 in one of the links

https://www.google.com/search?q=TSM+OEM+%23+68920+-01B

and

https://www.google.com/search?q=2004+Harley+road+king+custom+needs+a+new+TSM

..

Drag Specialties is a good start for aftermarket parts.

I ran your VIN through Motoverse...
VIN: 5HD1FRW135Y700148
World region: North America
Manufactured in: USA
Year: 2005
Make:
Harley-davidson
Model:
FLHRCI = Touring Road King
Body style:
Road / Street
Drive type:
RWD
Cylinders:
2 Cylinders
Engine type:
Fuel-injected Big twin

Big tip 'o' the hat to harleyds96 for giving me the impetus to get after it and tear the lamp down and sort it out. You'll need a precision Phillips #1 screw driver to remove the 8 screws. You'll have to pry the 4 little rubber pads off that double as screw hiders
Once you've carefully separated the bottom plate from the rest of the pedestal, you'll see that you need an extra set of hands to hold the plate, amber glow ring, and the main lamp body with, while you fight with the little fuse box in the center of the lamp.
They all have to be held, because the speaker wire runs through the amber ring to the bottom pad, and can't be unplugged, 'cuz it's soldered. No spade connectors, nah, that'd be too easy - and complicated. They'd like to make it so much easier to toss out another $80 for a replacement, 'cuz you stupidly lost the receipt!
So now that you've got everything separated, you discover that there's another two screws holding the ends of the fuse box to the main body of the lamp. Yes, they must be taken out too, so's you can properly fight with the four little clasps holding the fuse box together!
If you can get it popped open without ripping wires from their solder connection, you're a neurosurgeon! I lucked out, 'cuz I did the operation whilst sitting at the computer desk, so the bottom two pieces could rest on it, without ripping the speaker wires off of the speaker, while at the same time, the main body of the lamp was resting in my lap.
Now that you've succeeded in getting the box open, you'll see that you have that little fuse there, that the Harley lady mentioned above found. It's stamped - 1A/250 V, which, I suppose, would mean it could be plugged in down undah, where they use 240 volts.
So I'm going to see if I can find a 2A/250V fuse somewhere, and if that's too hot for it - TOUGH! I'll have a Harley Davidson plastic patty melt! vonster.vaughn