The measurable position of a black hole's event horizon

I'm imagining a static context where you have a large black hole that doesn't change in size or mass and isn't rotating (i.e. a hypothetical situation). It has an event horizon which, from a certain distance, you are able to measure an exact location for. My question is, if you moved much closer to that exact location (and hence began to descend much deeper into the black hole's gravity well) would the location of that event horizon measurably change (with respect to you, the observer)?

I guess part of this question is whether, as an observer, an event horizon is always going to be a bit further beyond where you are - i.e. you can never know that you have 'crossed' an event horizon, with respect to what an distant observer may surmise.

Thanks!