I have another type of gateway 2k keyboard from the mid 90s with a similar design (rubber dome, flex circuit, same manufacturer but the layout is a conventional keyboard layout). Every once in awhile several of the keys including the down directional arrow will stop working and the quick fix is to press down on the plastic keyboard top shell roughly in the vicinity of where the connector on the flex circuit connects to the cable (in my case, this is around the top of the numeric keypad and I press down firmly on the casing with a finger underneath the page down key and maybe also and the / key (it's a similar connection as the anykey, I think the internal connection partially relies on a piece of foam to sandwich the flex circuit connector to the connector on the cable and the foam may break down from age). It's also helped me with this issue to not use the kickstand legs of the keyboard, so it is flatter on the desk.
Alternatively, I've had good luck tightening the screws in the screw posts near that area of the keyboard, like even if I thought they were already tight, just tightening them slightly more, and having that make things work for a good while. Eventually the non responding keys issue comes back but when either pressing on the keyboard shell or tightening a case screw fixes things for weeks at a time, I can live with it. Id definitely focus on that connection point if looking to do a repair and the flex circuit looks reasonable.
I've taken mine apart before but nothing really looks odd or like it could be easily improved to get a better connection than it's already getting. These are cheap quality keyboards with cheap components and I only use mine so I have a matching logo/design with my gateway 2k PC 😂