so do the versions GOG sells have support. I have medical reasons not to be using a keyboard and mouse for the time I like to spend on these games.

Probably not any more than the versions you already have. Have you looked into mods or external programs that may be able to add such support?

I haven't found one that works.

Can't help personally (I don't own Oblivion, and have never tried to play Morrowind with a controller [which I don't own anyway]), but maybe someone else will have some suggestions.
You may also want to ask around on Steam, maybe a subreddit or two, etc.

Have you ever tried to search the internet for "morrowind controller" or "oblivion controller"? There is a number of suggestions.

Not sure why you pinged me for that... ;)

Apologies. I had clicked "reply" on your post, noticed my mistake, and deleted the qote copied from your post into my new one. Thought this was enough, but apparently it wasn't. Sorry again. :-)

Morrowind don't support controllers, until you use OpenMW.
In any case, OpenMW is the best way to play Morrowind nowadays. Stable, fast, lot of "quality-of-life" features like "virtual filesystem" for mods, custom (bigger and clear) tts fonts, 3rd person camera zoom, etc. And it's compatible with GOG-version.
Controller support still don't perfect, like in Xbox version. Your can't navigate in GUI with D-pad in current OpenMW builds, only with analogue stick.
You will have problems with OpenMW only if you need lot of incompatible mods like "Building Up Uvirith's Grave" forks.. If you just need some essential mods like "Patch for Purists", "Better Bodies"/Clothes/Heads, ESRGAN textures - it's works perfectly fine.

Oblivion, formally, support controllers, but in practice it's nearly unplayable with any of modern controller, until you use software like Xpadder or Logitech profiler. You can get used to it, but the controls are clumsy.
GOG version still better that steam, coz it's not require launcher, but still support OBSE. Xpadder, Pinnacle Game Profiler (not free), Logitech Profiler (free, but only for Logitech gamepads). etc.
Personally, I played Oblivion with old (freeware, via XP-compatibility mode) version of Xpadder. Probably not the best way, but it works.
By the way, you need to disable the controller support in the config.
bUse Joystick=0 in Oblivion.ini

Sorry this is so late, but Oblivion now has native Xbox controller support via the mod NorthernUI. Look it up on the Nexus. The latest build of Daggerfall Unity also now has full controller support. Morrowind lags behind, but OpenMW does have some level of controller support.