The length of time that a volcanic eruption impacts the climate is largely determined by

The length of time that a volcanic eruption impacts the climate is largely determined by  whether the ash or gas reaches the stratosphere

Explanation:

A volcanic eruption releases gases and other particles in the atmosphere. The factor whether these released material reaches the stratosphere or not, determines whether that particular volcanic eruption will affect the climate or not.

The enormous output from the eruption gets released in the atmosphere. This output forms a permanent layer in the atmosphere over time and becomes a barrier to the sunlight reaching the earth.

The decrease in sunlight causes cooling effect thereby decreasing the temperature of the planet.

The time taken by the emission to reach the stratosphere determines the time taken by the emission to change the climate of the planet.