The invention of the first gear shift cable is commonly attributed to the engineering advancements in early bicycle design. The key breakthrough for gear shifting on bicycles came in the early 20th century.
One of the earliest examples of a gear shift mechanism with cables was introduced by Campagnolo, an Italian company, in 1937. They developed the "CAMPAGNOLO cambio," which utilized a system of cables to shift gears. It wasn’t until later in the 1950s and 1960s that the more widespread use of gear shift cables in bicycles and automobiles became standardized.
While there isn’t a specific person credited with inventing the cable itself, these developments by companies like Campagnolo in the cycling world were a major step forward in the integration of cables for shifting mechanisms.
In terms of automobile gear shifting, the development of the cable mechanism evolved over time through contributions from many engineers, as the technology improved for smoother and more reliable operation.