Good question! So the duration of the ground motion in a specific place is not usually directly related to what we would call the "source time function" (STF), i.e., a description of how long the earthquake rupture on the fault took to occur.

Let's first consider the STF, this is typically considered in terms of moment rate per time (e.g., Figure 2 in Vallee, 2013) where the total seismic moment released during an earthquake (which directly relates to the mangitude, i.e., the moment magnitude) is effectively the area under a STF curve. From figure in the linked paper we can see that the same magnitude earthquake can have different patterns of moment release (i.e., Figure 2 a-c are all the same magnitude events and thus released the same total moment, but with either ruptures that occurred more slowly or quickly so moment rate varies between them). There are a variety of details of an earthquake where the STF is important, but as we'll see, duration of ground shaking at a location is not usually one of them.

If we shift our attention to the duration of ground motion, we can consider a range of empirical equations that have developed to try to estimate duration of shaking, specifically Table 1 from Yaghmaei-Sabegh et al., 2014, we can see that total moment (in the form of moment magnitude) appears in all of these equations, but none of them directly consider anything about the STF or speed of the rupture in a formal sense. Instead, you'll see that in addition to the magnitude, there are few other general earthquake properties (e.g., depth of the hypocenter), but then a lot of things specific to the "site" you're considering, both in the sense of things in relation to the specific earthquake (e.g., distance from the rupture) but also more generally (e.g., soil type, etc.). This reflects that broadly, while there are obvious controls from the available seismic energy (which will be dictated primarily by the total moment, i.e., magnitude, and the sites distance from the source), there are also a lot of site effects which can impact duration of shaking (and other important details, like peak ground acceleration, dominant period of the shaking, etc). In detail, the type of rocks and their geometry can play a large role in the specifics of shaking in a particular place. E.g., seismic waves in sedimentary basins tend to "reverberate" and thus the duration of shaking can be significantly longer than outside the basin and as they reverberate, they can have both constructive and destructive interference with each other and in many cases can amplify shaking at particular frequencies (which is very important to understand if you're trying to engineer a building to survive an earthquake).