I'm working on a TTRPG system that takes place about a century after an apocalypse event. I've hit a point where a bit of world building is required, and so I'm going down the list of technologies (electricity, medicine, radios, etc.) that could be viable without significant industrial activity. For context, most settlements house less than 500 people, are not part of inter-settlement organizations, and are mostly agrarian. I won't go too deep into the specifics, as it isn't super relevant to the question, but large settlements are often squashed and invaded. This means that industry is slow to take hold and very rare.
Now, to my main question. Would it be possible for individuals/settlements to create rudimentary motor vehicles, such as buggies and motorcycles, under these conditions? Obviously, any pre-apocalypse vehicles would be rusted away and unusable, and gasoline would have rotted. My idea is that the engines would run on vegetable oil, as most settlements are very agrarian. However, I'm not convinced that the settlements would have the manufacturing capacity to make combustion engines in the first place.
Any help with this conundrum would be appreciated.