Having designed 3-axis accelerometer and inclinometer modules for a variety of applications, I can tell you that the most straightforward and mechanically reliable approach will be to use a 3-axis accelerometer. Detect the 1G gravity vector, then watch for changes along that vector to indicate vertical motion. I presume it is unlikely that you can keep the sensor perfectly orthogonal to gravity, so you cannot ignore the "other two axes"... you will need to do 3D coordinate rotations and some filtering to differentiate between orientation changes and actual vertical movement.
None of this is overly difficult, and will yield a sensor with no moving parts (other than the internal MEMS element) that requires no maintenance.