I have managed to create my first Mosaic using the scheduler. Much easier to do than I had anticipated, the Scheduler is pretty smart!
I did this mosaic as an experiment with only 15 short frames per tile, 2x2 matrix, so it was all done in one evening.

Now I want to do a mosaic over 4 evenings. What is the best way to set it up so I can trigger each tile manually and shut down so I can continue the next day (hopefully!).

You don't need to start/stop each tile manually. You can setup the number frames for each tile, save the schedule to a file and reuse it until very night until it is complete. It will automatically start from the last uncompleted tile each night.