I plan to take a day trip from Zurich to Pilatus on 13th May. I wanted to book the Golden round trip. However, it appears the first boat starts at 10.38 am (Lucerne to Alpnachstad) based on the timetable (https://www.pilatus.ch/en/inform/timetable). However, the Pilatus.chh website allows me to reserve the seat on the cogwheel as early as 8.10am or 8.45am from Aplnachstad. Can someone help me to understand why? Is there an early boat to catch early cogwheel train?