When you try to build a light.. look at what it takes to build the item. If you have greyed out (slightly darker) item in list then you should see an option down below to "search" that will put a magnifying glass icon next to the lacking material. I am going to say at a guess ... Copper..
You need the materials to be able to build the item.
Failing this.. Try going to the work bench and activating build mode from there.. Failing that fast travel else where then come back. Thats what will cover any small glitches. Otherwise idk. If you can bring up build mode then you should be able to build. if you have the materials.
Failing all that try saving game then restarting and just hope that wont become a frequently needed fix solution..
also last edit here- you may have the stuff at other settlements but not here.. You may want to set up a supply line. Good luck mate!