You need to use ePub as a format to mark the correct items semantically - Calibre triggers off these semantics during conversion to mobi. HTML doesn't have ebook semantics, it's just html.
When you use ePub, your ePub TOC in Sigil will equate to where the tic marks show up on the Kindle for navigation. The inline user visible TOC is the one you will create by hand.
Here's the post describing how to make your hand-edited TOC the one that's used as a Kindle TOC:
https://www.mobileread.com/forums/sho...0&postcount=11
And here's the thread on controlling the start point:
https://www.mobileread.com/forums/sho...ght=mobi+start
If you go through the Sigil forum there are descriptions there about how the power users go straight from text editors to Sigil for final tweaking as an ebook.