Here's a picture of the back of a later-model GMT400 cluster (with credit given to
@5vortec7)
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In this picture below, I've circled but a few of the many lightbulb sockets. These are twist-n-turn sockets, simply grab them with your thumb-n-finger to loosen and remove. Notice some are big and some are small, and even the colors are different (grey, white, black).
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I believe the bulbs are some sort of special, long-life type because most of them seem to last almost the life of the vehicle. (edit: See
@Caman96 's post following this one /edit)
Replacement bulbs can be found, e.g., on RockAuto (look under 5.7L V8 > Electrical-Bulb & Socket > Instrument Panel Light Bulb).
ALSO, if you look closely at the bulbs as you remove them, you may see markings on them indicating the bulb part number, e.g., 74, 161, 193, etc. Those markings are your best clue to use for finding replacements.
The "long life" bulbs are typically indicated in their part numbers with an "LL", e.g., a 193-type bulb in "long-life" version will have part number "193LL". When you go shopping for bulbs, consider looking for the "LL" versions.