Ah. Okay. So, yeah, a problem with the *keyboard* ROM would indeed probably roughly match what I'm seeing. Unfortunately on the IIgs there is no separate keyboard ROM; instead there's a microcontroller with 3K of ROM built into it that controls the keyboard and the ADB bus. If that's the problem I know of no other source for that IC other than another IIgs and getting it off would require surface-mount rework skills I don't have.
(In theory the microcontroller was available as a "generic" part from Mitsubishi and the ROM image is in the wild, but you'd have to find an EPROM-programmable version of it in a compatible package, program it, desolder the old one...)
In my mind the only hope is if there's some external problem that might be causing the keyboard controller to "flake out", IE, reset, perhaps?, because it's receiving insufficient voltage, or something else along those lines.