“Small“ was a requirement, but perhaps mini DIN would work.Although it has nine pins and you only need three pins, the old computer "D" style connectors are often available on used and scrapped items. They offer the benefit of a solid connection, backshell options for wire strain relief, optional screw locking, and common availability. In addition they are often available with cables attached.
Of course, in some areas no obsolete or discarded hardware is available.
A second common alternative is the five-pin (DIN) circular connectors such as have been used for both keyboard and audio connections for many years. They are an easy to handle size and big enough to be easy to install without needing a magnifier. And they do not match any of the current products so accidents are much less likely.