Topoelectrical circuits are metamaterial realizations of topological features of condensed matter systems. In this work, we discuss experimental methods that allow a fast and straightforward detection of the spectral features of these systems from the two-point impedance of the circuit. This allows us to deduce the full spectrum of a topoelectrical circuit consisting of N sites from a single two-point measurement of the frequency-resolved impedance. In contrast, the standard methods rely on N2 measurements of admittance matrix elements with a subsequent diagonalization on a computer. We experimentally test our approach by constructing a Fibonacci topoelectrical circuit. Although the spectrum of an infinite Fibonacci chain is fractal, i.e., more complex than the spectra of periodic systems, our approach is successful in recovering its eigenvalues. Our work promotes the topoelectrical circuits as an ideal platform to measure spectral properties of various (quasi)crystalline systems.