Using a novel apparatus coupling a visual illusion with an eye tracker device, trained participants are able to generate smooth pursuit eye movements, even without a target to follow. This allows them to perform arbitrary continuous shapes, and, for instance, write letters with their eyes. In a previous study, based on data from a single writer (author JL), we developed and tested a Bayesian computational model -- the BAP-EOL model -- able to simulate character recognition. In the present study, data from different writers provide the opportunity to study the signal characteristics of eye-written letters. More precisely, we extend the model to perform writer recognition. Experimental results, and high performance we obtained, show that eye writing is as writer specific as handwriting is, and that motor idiosyncrasies are present in eye-written letters.