There are many points to consider when looking at a bike for downhill handling characteristics. First look at the wheels, spokes, nipples, rim, tire and tube weight. Having raced downhill (mountain bikes) since the early 90s the first thing I did to increase stability on high-speed descents was to use heavier wheels. These two items are gyroscopes; so increased weight will yield increased stability. A lower bottom bracket will make a bike descend with more stability because of the lower center of gravity. This was very evident in the late sixties and early seventies when road bikes started seeing more track bike like geometry. The reason for the change here was the popular Criterium races taking place in this country. More pedal clearance was needed for the tight turns among a few things. Fork rake, head angle and wheel base length also play a large factor here. Check where your center of mass is in relationship to you bottom bracket and last, but not least, check you level of drop from the seat to the handlebars. The more forward your center of mass is on the bike will make the bike feel more skittish. And just one more thing, carried weight, while generally not a consideration with day tripping and short rides, the higher carried weight sits on the bike will make it feel more skittish as well.
Hope this helps and hope it doesn't go against the general vintage topic of discussion that should be taking place here. I did think that it brought up a good point, although at first might not be realized, the change in geometry that took place in that time period.
Mark, bright and sunny and looking forward to spinning today, Poore