Future automated vehicles may be equipped with external Human-Machine Interfaces (eHMIs). Currently, little is known about the effect of the perspective of the eHMI message on crossing decisions of pedestrians. We performed an experiment to examine the effects of images depicting eHMI messages of different perspectives (egocentric from the pedestrian's point of view: WALK, DON'T WALK, allocentric: BRAKING, DRIVING, and ambiguous: GO, STOP) on participants’ (N = 103) crossing decisions, response times, and eye movements. Considering that crossing the road can be cognitively demanding, we added a memory task in two-thirds of the trials. The results showed that egocentric messages yielded higher subjective clarity ratings than the other messages as well as higher objective clarity scores (i.e., more uniform crossing decisions) and faster response times than the allocentric BRAKING and the ambiguous STOP. When participants were subjected to the memory task, pupil diameter increased, and crossing decisions were reached faster as compared to trials without memory task. Regarding the ambiguous messages, most participants crossed for the GO message and did not cross for the STOP message, which points towards an egocentric perspective taken by the participant. More lengthy text messages (e.g., DON'T WALK) yielded a higher number of saccades but did not cause slower response times. We conclude that pedestrians find egocentric eHMI messages clearer than allocentric ones, and take an egocentric perspective if the message is ambiguous. Our results may have important implications, as the consensus among eHMI researchers appears to be that egocentric text-based eHMIs should not be used in traffic.