Hi TBM
First of all I know nothing about MGB'S so what I am about to suggest might not be practical. What I would do is first is remove the distributor cap so that the engine does not start. Turn the ignition key to start, does the engine turn over in a sprightly manner?. If so you can be fairly sure that the battery terminals are secure and the earth strap to the engine is good. refit the distributor cap. From the battery to the starter solenoid will be a thick cable to carry the starter current and I am guessing and it is a guess that from there will be a thinner cable to the fuse board to supply the fundamental power feeds via fuses to the various items, wipers, ignition, headlights etc.
In this problem there are two sources of power one is from the alternator supplying one side of the alternator bulb and the other from the battery supplying the other side of the bulb. So I would try and investigate the issue by eliminating one of the power sources i.e. lets first not start the car. hence only one power source, the battery and do some tests. If it is possible to get at the fuse panel where the main supply cable to the fuse box arrives, I would find a good earth for the Common or Negative of your test meter. Switch on the ignition and measure the voltage at the battery terminal and then with the negative of the meter still at the same earth point measure the voltage arriving at the fuse panel, or if you can get at it arriving at the live side of the ignition light. Are they the same? They should be within a few millivolts. Then with the ignition still turned on, turn on the wipers, are the two voltages still equal ? (they should still be) then turn on the headlights, are the two voltages still equal, they should be. If you find that as you increase the load i.e. turn on more and more items the voltages are getting gradually further apart, then you can be pretty sure that you have a bad connection somewhere between the battery + and your fuse panel. this would match the description you give of the ignition light getting brighter when you turn on more load, i.e. wipers and sidelights from your previous post. It would also kind of point to the fact that you mention, the fuse panel needs a bit of work. Bear in mind that I have never owned or been anywhere near an MGB GT, but if someone bought the car to me for some help, that is what I would be doing as a start to look at the problem.
Hope that this is of some help.
Regards ZACH
