This driving simulator study, conducted as a part of Horizon2020-funded L3Pilot project, investigated how different car-following situations affected driver workload, within the context of vehicle automation. Electrocardiogram (ECG) and electrodermal activity (EDA)-based physiological metrics were used as objective indicators of workload, along with self-reported workload ratings. A total of 32 drivers were divided into two equal groups, based on whether they engaged in a non-driving related task (NDRT) during automation or monitored the drive. Drivers in both groups were exposed to two counterbalanced experimental drives, lasting ~18 minutes each, of Short (0.5 s) and Long (1.5 s) Time Headway conditions during automated car-following (ACF), which was followed by a takeover that happened with or without a lead vehicle. We observed that the workload on the driver due to the NDRT was significantly higher than both monitoring the drive during ACF and manual car-following (MCF). Furthermore, the results indicated that shorter THWs and the presence of a lead vehicle can significantly increase driver workload during takeover scenarios, potentially affecting the safety of the vehicle. This warrants further research into understanding safe time headway thresholds to be maintained by automated vehicles, without placing additional mental or attentional demands on the driver. To conclude, our results indicated that ECG and EDA signals are sensitive to variations in workload, and hence, warrants further investigation on the value of combining these two signals to assess driver workload in real-time, to help the system respond appropriately to the limitations of the driver and predict their performance in driving task if and when they have to resume manual control of the vehicle.