I think they carry on all the way to where Green Lane station is, think they are what is on the bridge over Green Lane, if you look on Google Maps/ Earth you can follow them.
They do indeed go to Green Lane & then on to Rock Ferry. You can still see them from the Merseyrail train between Rock Ferry & Green Lane, on the river side. On this map, after crossing Green Lane, a line goes off to the left to Mollington St. sheds, then several lines go off to the right into Laird
's & some carriage sidings. At the very top of the map, the remaining lines split; those on the right go to Town Station & Woodside, those to the left are the lines to the docks, through the Haymarket tunnel, recently re-visited by a team of intrepid explorers.(See the thread in Urban exploration).