Blood plasma viscosity (PV) is an established biomarker for numerous diseases. Measurement of the shear PV using conventional rheological techniques is, however, time consuming and requires significant plasma volumes. Here, we show that Brillouin light scattering (BLS) and angle-resolved spectroscopy measurements of the longitudinal PV from microliter-sized plasma volumes can serve as a proxy for the shear PV measured using conventional viscometers. This is not trivial given the distinct frequency regime probed and the longitudinal viscosity, a combination of the shear and bulk viscosity, representing a unique material property on account of the latter. We demonstrate this for plasma from healthy persons and patients suffering from different severities of COVID-19 (CoV), which has been associated with an increased shear PV. We further show that the additional information contained in the BLS-measured effective longitudinal PV and its temperature scaling can provide unique insight into the chemical constituents and physical properties of plasma that can be of diagnostic value. In particular, we find that changes in the effective longitudinal viscosity are consistent with an increased suspension concentration in CoV patient samples at elevated temperatures that is correlated with disease severity and progression. This is supported by results from rapid BLS spatial-mapping, angle-resolved BLS measurements, changes in the elastic scattering, and anomalies in the temperature scaling of the shear viscosity. Finally, we introduce a compact BLS probe to rapidly perform measurements in plastic transport tubes. Our results open a broad avenue for PV diagnostics based on the high-frequency effective longitudinal PV and show that BLS can provide a means for its implementation.