You can get by with as little as an LED and a "watch battery". That's all that is in some teeeny flashlights, anyway. Just make sure that the LED needs a bit more voltage than the battery can deliver, for long LED life.
F'r instance, if you are using a BLUE or WHITE LED, they need about 3.6 volts to operate at full brightness. So use a watch battery that puts out 3 volts. How? The LED will have two leads coming out of it - one needs a POSITIVE connection, the other needs a NEGATIVE. The flat top of the battery is one connection, the other flat side is the other. Slide the leads from the LED onto the top and bottom of the battery, and if it doesn’t light up, flip the battery over and that will reverse the connections. Remember which is which - the case of the battery is often marked for polarity. On most new LEDs the leads are two different lengths - the shorter one is usually the NEGATIVE one.
If you want to use a RED, AMBER, ORANGE, YELLOW, or most GREEN LEDS, they take between 1.8 and 2.6 volts, so you can use a 1.5 volt watch battery and see how the LED lights up.
Older LEDs may not be as efficient as newer models, so you might see if you can find “super bright” LEDs in the size and color you need - they may operate dimmer than their full brightness at their full voltage, but still be usable at lower supply (battery) voltage.
LEDs come in many many sizes and shapes, usually as a tiny crystal embedded in a bubble of clear epoxy. That epoxy bubble can be shaped, as long as you keep enough ‘body’ to support the leads, and don’t get too near the crystal and the hair fine wire connecting it to one of the leads.
You might look at ‘Surface Mount’ size LED if you really need a small one. Try Ngineers N gauge model railroad supplier for truly nano sized ones.
You can just leave a space to slide the battery into the figure to turn the LED on or off. Like in a back pack, or in the base.
I've put LED eyes in a 25 MM gargoyle, and a 'flame' in the staff of a 25 MM wizard, so it is doable!
HTH
