Drought is a powerful natural hazard that has significant effects on ecosystems amid the constant threats posed by climate change. This study investigates agricultural drought in a semi-arid Mediterranean basin through the interconnections among four indices: precipitation (meteorological reanalysis), vegetation development, thermal stress, and soil water deficit (remote sensing observations). While drought seems to be a clear concept with effective assessment tools (e.g., SPI and SPEI), the definition of drought periods is blurrier. This article examines the main drivers of agricultural drought, precipitation, soil moisture deficit, incipient vegetation development, and rising soil surface temperature. Their temporal connections in various agrosystems of the basin and the determination of drought periods by revisiting the run theory were investigated. The Pearson correlations at different spatial scales showed a medium to low level of agreement between the indices, which was explained by the geographical heterogeneity and the climatic variability between the agrosystems within the basin. It was also shown that the cascade of impacts expected from lower precipitations was revealed by the cross-correlation analysis. The connection between precipitation deficit and vegetation remains significant for at least one month for most pairs of indices, especially during drought events, suggesting that agricultural drought spells can be connected in time through the three or four selected indices. Short-, mid-, and long-term impacts of precipitation deficiencies on soil moisture, vegetation, and temperature were revealed. As expected, the more instantaneous variables of soil moisture and surface temperature showed no lag with precipitation. Vegetation anomalies at the monthly time step showed a two-month lag with a preceding effect of vegetation to precipitation. Finally, the determination of drought events and stages with varying thresholds on the run theory showed large variability in duration, magnitude, and intensity according to the choice of both normality and dryness thresholds.