Wave localization has been extensively studied for over a century in various physical domains, including electromagnetism, elasticity and acoustics. In particular, the fundamental interplay between local properties (material composition and geometrical architecture) and structural defects has been proven to lead to the emergence of localized modes offering intriguing possibilities for spatial wave control. However, despite the variety of designs proposed so far, most of the approaches derive from contextual modifications that do not translate into a design paradigm. Few exceptions include designs endowed with topological dispersion bands, which, however, require changes over substantial portions of the structure. To overcome these limitations, here we introduce a new rationale based on real-space topology to achieve localized modes in continuous elastic media. We theoretically predict and experimentally demonstrate the spectral flow of a localized mode across a bulk frequency gap by modulating a single structural parameter at any chosen location in a mono-dimensional mass-spring chain with a defect spring arbitrarly located in the chain. The simplicity and generality of this approach opens new avenues in designing wave-based devices for energy localization and control.