What is the best pattern for opening Mega Nav on touch device when parent Nav items are link to landing pages?

I have a mega menu opening on desktop, on hover over a parent nav strip. The parent nav items are links on click.

The same menu is to be used on landscape tablet. Without on hover, click is used to launch the mega menu. So we lose the click to launch the parent nav linked page.

What is the best pattern for this? (I've seen a tap and hold open the menu on some sites, with quick tap to launch link).

For keyboard only navigation what is the best alternative to Enter, after tabbing to the parent nav item, to launch the menu? Down cursor?