The Patty Duke Show, 1963-66. The theme song explains it all, mostly. The “identical cousins” came about because their fathers were identical twins. Just FYI - Patty wears the headband, with her hair turned under, while Cathy wears it turned out - except when they’re pretending to be each other.
Meet Cathy, who's lived most everywhere,
From Zanzibar to Berkeley Square*
But Patty's only seen the sights
A girl can see from Brooklyn Heights -
What a crazy pair!
But they're cousins,
Identical cousins all the way.
One pair of matching bookends,
Different as night and day.
Where Cathy adores a minuet,
The Ballets Russes, and crepe suzette,
Our Patty loves to rock and roll,
A hot dog makes her lose control -
What a wild duet!
Still, they're cousins,
Identical cousins and you'll find,
They laugh alike, they walk alike,
At times they even talk alike -
You can lose your mind,
When cousins are two of a kind.