Although an undulating cab isn't as scary as death-wobble steering, it is annoying. Excessive bodyroll and clunking during cornering could mean shot body mounts.
Stock-style rubber mounts are quiet and compliant. However, they deteriorate over time. Polyurethane replacements resist chemicals and contaminants, but they have a reputation for being harder.
Replacing cab mounts is like doing a body lift, only on a smaller scale: generally no line or linkage disconnecting is required. Replacement pickup body-mount kits normally only have cab parts (the bed bolts directly to the frame); SUV kits have additional spacers. The Daystar Cab Mount kit shown here for '72-'80 Chevys reuses most of the stock hardware.
Cleaning the OE parts with a wire brush or wheel is advisable. Severely corroded parts should be replaced. Overall, this is an effective, relatively easy fix for cornering "whoas."