Zero-field muon-spin-rotation (μSR) experiments and the observation of a spontaneous Nernst effect indicate broken time-reversal symmetry (BTRS) at T Z2 c, slightly above the superconducting transition temperature Tc in Ba1−xKxFe2As2, with x ∼ 0.8. This was interpreted as evidence of a distinct state of matter where BTRS above Tc arises from noncondensed Cooper pairs, which maintain long-range interband correlations. However, an inhomogeneous superconducting state competing with magnetism as the origin of the observed behavior cannot be completely ruled out to date. Here, we present detailed 75As nuclear magnetic resonance (NMR) measurements of Ba1−xKxFe2As2, with x = 0.766, yielding T Z2 c > Tc. The NMR data demonstrate that the superconductivity is homogeneous throughout the entire sample volume despite the occurrence of nanoclustering of Ba/K atoms. We observe a suppression of the spin-lattice relaxation rate 1/T1T below the characteristic temperature T ∗, well above Tc. The specific heat yields somewhat lower values of T ∗, consistent with the microscopic theory of electron quadrupling. The observed monotonous suppression of T ∗ and T Z2 c in applied magnetic field, the overall temperature dependence of 1/T1T, the NMR spectral characteristics, and the μSR Knight shift rule out spin magnetism and the proximity to a magnetic instability. We conclude that our data indicate the appearance of pairing fluctuations below T ∗ and that the breaking of time-reversal symmetry represents an unconventional state which is unrelated to spin magnetism.