Eggcrate displays first appeared on Temptation in 1967. They were a lot different from today's version, though...
First off, they could only display the numerals 1, 2, or 3.
Secondly, the 3 looked different. It wasn't apparent until The Joker's Wild pilots, but the 5 looked different as well.
The early eggcrate displays, as shown on Temptation and the 1969 pilot of The Joker's Wild.
In 1971, Password refreshed their set, with new scoreboards and a digital time clock for the bonus word. These eggcrate displays are close to the modern variant.
The modern eggcrate displays, as shown on the 1971 version of Password.
From then on, more shows such as The New Price is Right and Match Game used the modern eggcrate displays for scores and timers.
The Price is Right is currently the only show that uses this display type.