[Note form JA: Both of these puzzles appeared in the same week. The theme reveal in both puzzles is exactly the same. Since puzzles are scheduled months in advance, this is really an amazing coincidence.]

NY Time Crossword
August 11, 2020
Amanda Rafkin and Ross Trudeau

What do the following phrases have to do with a children's song?

1. DERRINGER PISTOL
2. REWRITES HISTORY
3. PRESIDENT WILSON
4. VERMICELLI BOWLS
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LA Times Crossword
August 13, 2020
Jeffrey Wechsler

What do the following phrases have to do with a children's song?

THE BEST INTENTIONS
THE TIME IS NOW!
NEW DIRECTION
EITHER WILL WORK

Answers to both puzzles:

They each contain the vowels EIEIO in that order and with no other vowels.*

*EIEIO is the refrain from the song "Old McDonald Had a Farm."