Evans Designs has some great stuff. They have pre-wired LEDs which you can hook directly up to a battery
If you wanted to hide that in the kit, I would probably go with the 3 volt option as you can use those small flat round "watch" batteries
Going with the size of the kit I would probably use something like this
Possibly the pico
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The wires are super thin and you should easily be able to find room and bend/position as needed
And the holder for a 3 volt cr2032. Has an option to add an on/off switch also
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The only possible downside is if you are looking for a rounded edge to appear like a lens Those LEDS are flat, but they are plenty bright despite being small
You could possibly try one of these
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However, I think the 3mm would be too big and bright, the 1.8 mm might be ok, but you may have a hard time bending the resistor/connector part in the black shrink tubing to the angle needed in the head.
You could wire you own and put a resistor further down though