You can get a
nice daily driver condition 80s Mercedes diesel for pretty cheap. Like $5K-10K. The few electronics in the car are analog. There's a really cool (but kind of frustrating) vacuum system that handles
a lot of what electric cars handle. Smooth ride and deceptively quick cars once you get past the turbo lag.
Another option to look into is >25 year old imports. That is the timeline where many of the prohibitively expensive import duties lapse. Serendipitously this means all the
no-electronics models will be available. Even late 90s or early 00s JDM-spec cars are going to be more in line with the "digital luddite" kind of design philosophy. There might be a computer but it's only going to be able to "talk" over something like OBD ports, if at all. You're far more likely to find clever analog components and relays and shit. You would have issues potentially with something like an EMP, but the CIA glowniggers won't be able to make you do something like accelerate into a tree at 90mph. I'm personally waiting until hopefully 2027 to start importing as many 2002+ 4runners/Hilux Surf's I can but that's definitely too electronic-y for Null's purposes.
@Sneeds makes a solid recommendation. The 7.3 is a legendary diesel and even the 351W for gas is not bad to work on. These are great trucks if you've got a u-pull-it yard nearby. If you look for these try and avoid lift kits in general or at minimum avoid huge ones. There's some "creative" engineering going into a lot of the more rigged kits. You're better off avoiding someone else's mistakes.
If the budget could stretch to something like $20K you start getting into really fun options like a tube-chassis dune buggy. I've even seen some where they elected to use air cooled VW engines. It's hard to get more bare-bones and mechanical only than that.