Georgina,
While I as a German did prefer scrutinizing the original 1905 Elektrodynamik paper, you gave a good hint to an excellent translation where e.g. I. Kinematic Part, §1. Definition of simultaneity begins (within number [8] on the right side of page) with introduction of coordinate systems, at first such a system at rest. Then the notion time is meant as what the clock usually reads simultaneous with a particular event. Einstein then questions the ubiquity of time, your unitemporal Now, Georgina.
Perhaps, he was influenced by Poincaré's "local time". In [10] he is accordingly using A_time and B_time as well as a desired time common to A and B as coordinates. In the following definition time means something quite different, the timeSPAN "needed for the light to travel from A to B" or vice versa.
To be continued
EB