Hello and welcome to Electronics Point
First, I have to know if you are the Crash Test Dummies bassist or not... Perhaps you're a fan and you're using his name?
As Gryd3 says, you can't use the signal itself to power the LED - there's not enough energy, for a start. So some kind of battery
would be needed, and that will determine the minimum size.
Assuming you have a power source, electrically you can distinguish three states for a guitar cable: (1) not plugged into a guitar, (2) plugged into a guitar with no signal, and (3) plugged into a guitar with signal. These states could be displayed with a multi-colour LED.
This assumes that the guitars have a DC path. They normally do, but it's possible for an active or passive guitar or bass to include a DC blocking capacitor in series with the output. I haven't seen this, but I haven't seen inside that many instruments. In this case the guitar's presence couldn't be detected unless the guitar was modified. The signal could be, though.
Circuitry to do this could be made fairly small, but not small enough to fit into a plug. Even if tiny SMT (surface-mount technology) components were used, on a tiny, thin circuit board, the battery would be too big.
So you could make a small box that you could plug cables into, but that's not quick and convenient. You could make a number of small boxes that connect in-line with cables. The problem then becomes battery lifespan.
The monitoring circuit can be designed to consume very little current when the cable is not plugged in, so you could use, say, a 3V CR2032 button cell and it might need replacing every few months or after every ten gigs.
(Re Adam's suggestion: parasite power is not used with guitars, but a monitoring feature like you want could be built into a DI box.)
Edit: I meant to say "phantom power" not "parasite power" there!
Feel free to tell us more about what you want.