The Hair Fair Barbie #4042, #4043, and #4044 was never sold with a body. She only had a head, hair pieces and hair accessories. These heads were meant to be replacement heads. They all had blue eyes, real rooted eyelashes with side glanced eyes, until set #4043 was re-released with center-glanced eyes. They were available in Blonde and Brunette. Set 4044 also had red hair. When you find this head on the secondary market, it is usually found on a twist n' turn Barbie Body.
#4043 (1969-1970) Hair Fair Barbie Set. This set was re-released again in 1974 but with center glance blue eyes.
#4042 (1967-1968) Hair Fair Barbie Set
#4044 (1971-1972) Hair Fair Barbie Set
came with center glance blue eyes
The set came with a fashion wig which came in 3 colors (blonde, brunette, or titian), and 3 hair pieces: braided switch (or fashion switch), fashion wiglet, and long fall (or curly swirls). The names of the three hair pieces varied within the different sets. She had hair trim accessories in each set as well. #4043 only came with blonde or brunette hair. Titian colored hair pieces were added back in set #4044
Red hair pieces
#4043 Hair Fair Barbie on Twist 'n Turn Body dressed in #1454 Loop Scoop (1970)