This was also an issue I had in the 280zx, the original lights were as weak as p-ss, so I tried a heavier capacity globe, this caused the cut out effect as mentioned, the electrical system has an inbuilt load limiter
To remedy, I refurbed my spade fusebox and installed an Xenon set up with individual ballast units for each headlight, issue solved I now have lights as bright as a plane with less current draw than the original set up
As also mentioned good earth sectioning is essential in older cars, the more the merrier, I run my main earth to an engine mount and of course a newer heavier output alternator is of value