I don't know how long it's been this way, as I just noticed it, but the light at KPL doesn't work anymore.

I've read it has its own power, but the only light working is above the entrance.

I've tried running power to, in, and even attaching lights to the old light, but nothing is working.

Ideas to get it back on?

it only runs at night, is that it?

Actually, the lighthouse was lit up by the Glowing One inside the cage. Once you kill it and get access to the workshop, the lighthouse no longer shines like it did. Read the logs on the terminal in the house, explains it well enough.