$12k doesn't go that far these days, even for a 2+2 it will only get you a decent driver that has been relatively well kept, but rough paint, tired interior and dirty engine bay. Keep in mind that 2+2 values have been kept low for a long time and so many cars haven't been properly looked after as a result. This makes finding a good 1 hard.
Pretty rare to be honest, but maybe more likely than finding a 2 seater. For some reason 2+2's have lasted longer with the same owners perhaps because of the extra seats? This is really my anecdotal observation than hard fact, but I feel like most 240z's have been through many hands. Where as 2+2's were in the family a long time. Anything that is single owner, with original books, radio and carbs is now quite a find.
As you know, a restored car is going to be far cheaper in the long run. Some 2+2 bits and pieces are getting very hard to source, interior panels for example and rust repair sections need to be hand made and not available off the shelf. This is because 2+2's are relatively less common and have been less popular on a global level. A lot of reproduction parts now exist for 2 seaters but 2+2's are often forgotten. The cost of restoring a 2+2 and 2 seater is going to be pretty similar. The value of each when done though will be quite different.