First guess is that there is air in the damper and the clunk is the shock progressing undamped until the air is compressed and the piston hits resistance.
I can't feel that when compressing it in my hand, but presumably it'd be more obvious with the added leverage when on the bike?
Yep - on the bike your body weight and the leverage will make issues with the internals more apparent.
@TooTallTim started
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First guess is that there is air in the damper and the clunk is the shock progressing undamped until the air is compressed and the piston hits resistance.