From time-to-time I use Scenario Planner to create an all-stop service between Brighton and Haywards Heath and back using the 313. While not realistic compared to real life, it does provide a nice alternative away from regular passenger ops on East Coastway.
No. IRL the 313s run no services on the BML, just on the Coastway, but they do go home to depot along it as ECS moves, which is what the BML timetable reflects.
Mostly the 313s are stabled at Brighton (Lovers Walk) Depot, but they go up the BML to the other depot to get specialist technical servicing that Brighton can't do, and that's what's reflected in the ECS moves