You might like a Ford Fairlane 500. The car has a sort of industrial look and while this one is getting bid rather high you should be able to find one a little cheaper. The main problem with 60’s convertibles is finding one that is not eaten up with rust. Mechanically, they are all relatively simple.
You can’t get much more impractical than an early '60s Lincoln Continental or Cadillac Eldorado; monstrous slab-sided boats bigger than anything not registered as a “light truck” (and bigger than most light trucks) with gas mileage only slightly worse than pumping it directly onto the ground (but also loads of horsepower) due to 460+ cubic-inch V8s. They’re simple enough to fix yourself, and cheap to have somebody else do it. Parts aren’t quite as common as on the smaller Ford and GM engines, but readily available. Also, the Lincoln has the oddness points of being one of the only four-door convertibles, and the rear doors open backwards! Good unrestored ones usually go for $6000 or so.
If those are too big, I’d recommend a '65 Ford Galaxie or fullsize Mercury (Monterey, Montclair, or Park Lane, with the Marauder package [the equivalent of Ford’s “500”; race-inspired dress-up bits] a plus). They, especially the Fords, are relatively common and cheap.