Precision tests of first-row unitarity of the Cabibbo–Kobayashi–Maskawa matrix currently display two intriguing tensions, both at the 3σ level. First, combining determinations of V_ud from superallowed β decays with V_us from kaon decays suggests a deficit in the unitarity relation. At the same time, a tension of similar significance has emerged between K_ℓ2 and K_ℓ3 decays. In this Letter, we point out that a measurement of the K_μ3/K_μ2 branching fraction at the level of 0.2% would have considerable impact on clarifying the experimental situation in the kaon sector, especially in view of tensions in the global fit to kaon data as well as the fact that the K_μ2 channel is currently dominated by a single experiment. Such a measurement, as possible for example at NA62, would further provide important constraints on physics beyond the Standard Model, most notably on the role of right-handed vector currents.