Our 1981 380SLC did this
It ran so roughly it almost stalled.
Replacing the fuel injector holders/seals cured most of the problem - they were leaking. (125k and 20 years old). Inexpensive. 8 seals and holders are under $40 if you DIY. Job is similar to the 560 one on my site.
The local indy did a white smoke test (pumped into engine) and determined there were also intake manifold leaks. We still get some idle cycling, but I have yet to do the i.m. job.