I have two M.2 NVMe drives installed in my system, and booting from either one will load the grub from the eighth partition (an 18.04 install) of the second drive. I've confirmed this by looking at the /boot/grub/grub.cfg and it matches the contents of the grub menu.
As far as I understand how this works, this means that the EFI System Partition on both disks is "pointing at" nvme1n1p8.
I'm trying to set kernel parameters for the Ubuntu 20.04 install that I have on the seventh partition of the second drive, update-grub updates /boot/grub/grub.cfg there, but I can't access this menu (e.g. the menu that will show 18.04 as an alternative with the main top entry as "Ubuntu" (going to 20.04)).
I believe that all I need to do is run install-grub and pick which disk I want to overwrite grub with. It should cause it to point at nvme1n1p7 like I want.
However I am curious if there is some kind of a less intrusive way to perform this edit. Maybe I could go dig around in the efi partition itself and edit whatever specifies the 8th partition with the 7th partition... This would be handy if for whatever reason I wanted to check (without actually booting and testing) from a running OS which ESP points at which partition. I'm skeptical that this would be practical vs. just trying it. But I'm curious how it works. But I definitely won't bother if it involves hexediting.