Crossword Puzzle Bat eyelashes

Clue: Bat eyelashes

Bats one's eyelashes, say (FLIRTS with 6 letters)
Scene of a Tex. battle: 1836 (ALAMO with 5 letters)
C, in bathrooms (COLD with 4 letters)
Battle Born State: Abbr. (NEV with 3 letters)
Area away from the battle (REAR with 4 letters)
El ___, 1942 battle site (ALAMEI with 6 letters)
Mideast president who wrote "The Battle for Peace," 1981 (EZERWEIZMAN with 11 letters)
Man with a baton (LEADER with 6 letters)
Batted first (LEDOFF with 6 letters)
Gnats, rats and bats (PESTS with 5 letters)