We study the light scattering profile of a subwavelength layered gold-dielectric-gold nanosphere, which unveils exciting ultrasharp scattering-switching signatures based on high spectral proximity of the scattering resonance and cloaking states. Analytical expressions are derived for polarizability, resonance/cloaking conditions, and for scattering cross section of this layered metal-dielectric-metal (MDM) nanosphere, under the quasi-static limit. Our analysis allows one to thoroughly investigate its spectral response, over the entire parametric space of its dimensions and the incident light wavelength. Especially, the scattering spectra reveal multiple Fano-type, ultrasharp spectral profiles with high tunability, in terms of abrupt scattering-switching wavelengths and cloaking bandwidth, when absorption losses in the metallic layers are neglected in the analysis. Upon inclusion of bulk metallic losses along with enhanced electron surface scattering effects, these sharp spectral signatures are found to get severely faded in a realistic layered MDM nanosphere. The results obtained analytically, in each case, are found to be in excellent agreement with the numerical ones calculated based on Mie theory. We demonstrate that the ultrasharp scattering signatures of a pragmatic MDM nanosphere can be revived by introducing semiconductor gain inclusions in the middle dielectric layer, mitigating losses in the metallic layers.