The solution that I found is rather tedious.
It seems that, although Meshlab obviously uses these IDs under the hood, this information is not exposed to the user. So I following this heuristic:
- Choose the vertex of interest with the standard MeshLab tool.
- Invert the selection.
- Delete all vertices, and get an 1-point pointcloud/mesh as result.
- Export this as an .off file.
- Open the exported file and read the coordinates of this unique point. One coordinate (e.g. X) is enough.
- Search in your original .off file or in the original mesh/pointcloud structure to find the point/vertex with this coordinate.
- There you have it, you have the ID of the chosen vertex in the original structure.
- Then (this is application specific, according to my needs), using PCL, I created a Kd-Tree for my pointcloud, used the selected points (red) as "query" to get some nearest neighbors (green).
Result: