The F4 SHOOT lights only worked for me in the A2A training mission.
After that, no matter what multi-player server I was on, the SHOOT lights didn't work. I ensured I had the correct parameters to shoot: locked target, within range, Jester gave me the "one-one thousand" etc.
I then went back A2A training mission and they didn't work either.
I don't have any mods or anything. I also noticed my external tank lights don't work as well.