An agricultural header includes: a header frame; at least one cutting unit carried by the header frame and including a cutting element and a driveshaft coupled to the cutting element; and a gearbox configured to drive the cutting element. The gearbox includes a gearbox output rotatably coupled to the driveshaft; and a clutch including an intermediate shaft and at least one clutch shoe rotatably coupled to the intermediate shaft and displaceable between a non-engaging position where the at least one clutch shoe does not engage the gearbox output and an engaging position where the at least one clutch shoe engages the gearbox output. The clutch is configured such that the at least one clutch shoe displaces to the engaging position when a rotational speed of the intermediate shaft reaches a threshold value.