The closest you can get to TV and not actually be in TV, is Lakeside Landing in Oxford, FL. It's about 1 mile from LSL (Lake Sumter Landing Square). They have their own pool and are very close to Lake Miona State Park. You won't be able to use The Villages facilities such as playing golf or use the Rec Centers, but you can shop at the squares, eat at the squares, go to the movies and pay a $1 more, etc.
Lakeside Landing has a whole section of garage villas and usually they have a couple for rent. Here's one on Zillow for $1250 a month, which is cheaper this time of year than in TV. The development is on Rt 472, which is also Rainey Trail, the road that will take you right into TV next to Arnold Palmer Country Club.
Rental Listings in Oxford FL - 2 Rentals | Zillow
Lake Miona Park | Sumter County, FL - Official Website