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
Explore our collection of micro LEDs, including Pico, Nano, and Chip LED lights. Looking to brighten up your model project? We have the very best and brightest
evandesigns.com
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
Our 3-volt cr2032 battery holder and switch is a compact way to bring power to your 3-volt LED lights and brighten up your project. Shop online today at Evan Designs
evandesigns.com
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
12volt LED lights for modeling project, top-quality, affordable. Elevate your models with radiant illumination. Ideal for various DC-powered hobby applications.
evandesigns.com
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