Here are the N64 avatars that will be rolling out starting now:
Super Mario 64
Zelda: Majora's Mask
Nintendo 64 (hardware)
As of today, the rotation includes all of the above games in some capacity (though the hardware selection only involves three total images), so grab them while you can. These will be updated on a weekly basis according to the tweet, running through December 6: when the promotion ends. You can get them from the Switch Online app at the very bottom of your home screen, but you'll need to play for them with Platinum Points (all of them so far are 10 points each).
This week features a bonus array of points for playing Super Mario 64, Kirby 64, and Zelda: Majora's Mask on the N64 app: they'll grant you 100 Platinum Points each. The SNES bonus game is Panel de Pon, which is running in tandem with the 64 promos. Since the icon is in Japanese, look for this photo on the SNES home screen.