Replacing 23 year old 190 limiter for ceiling fan
I agree with JRaef the limiters were mandated by law and many fans were tossed when they failed, I know my personal fans do not have them a wire nut must have been installed by some gremlins or friendly elves In the night. The ones I have replaced red is hot white neutral black to the lamp and the lamp back to white.  There also ones that black and red are reversed so your particular model of limiter is needed to be sure. Whoops yours had blue and not black so the model will be needed to be sure. Wilt LED lamps they really are not needed , but prevent someone from putting in more wattage than the fixture is rated for.
Edit I did find one that was red input blue output and white neutral similar to the first one I listed but the part number should be checked because I have got them that the input and output were swapped