Those sort exist but the ones you can write with are generally too painful to carry. Because for them to work they need tiny batteries and tiny ink cartridges.You can't write with those.
And so you are constantly farting around either replacing one or the other.
But you get two sorts. One with a little torch on the back of the pen and one with an even littler torch on the front
A quick look. Olite do one. Which is at least a reputable brand.