1977 MG MGB Ignition/electrical

First if you have the amplifier in your distributor get rid of it as they are junk and fail without warning. It's easy to tell as it's electronic inside dist with a large box outside of it. Check your ignition switch wiring as there are no fuses or relays protecting the headlights and if you have put halogen lights in headlights there is a good possibility that you have burnt the harness from ignition switch to headlights inside the car. Ground are the largest problem on these there is a ground cable actually about three right by the coil area on the fender under the hood, clean that and make sure they are good. Also check the one in the trunk under the trunk latch as well. I have an 80 and used to own a 78 so very familiar with these. You alternator may be going bad why the light is staying on after key shut off but make sure with that prior to getting another. I highly recommend getting the MGB electrical systems by Rick Astley. It's about $60 but well worth it. It covers early and late models and by section so you know what to check very easy for the beginner. It is possible that you may need to run a separate ground to one of the lights to work.