The loose shock mount bolts that Elliot describes are a known issue but usually make the clunk sound heard his video rather than a squeak. If you have a definite squeak, I would look to the springs themselves. The original springs had 3 zinc interleaves (thin strips of zinc) between the 4 largest/longest leaves that was supposed to act as a lubricant, so the leaves slipped past each other with less friction. This reduced wear on the leaves and prevented squeaks. Many earlier large cars of the era, like Jaguar saloons, had leather gaiters over the springs so they could be greased regularly - the zinc strips were less maintenance and didn't require regular applications of grease. Replacement springs these days don't have those zinc strips but it is possible to dismantle the springs and install strips yourself if you want. To test if this is the source of your squeak, try spraying the ends of the largest leaves with penetrating oil (recognizing most penetrating oils aren't really very good at oiling things so any improvement will probably be short lived.
They are hard to see, but in the first picture, the top spring is as received and the lower one is after I installed the zinc strips