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Its listed in points at the back, but not as an entry for the faction; do they just take the tech marine from the generic chapter?

I guess?

Yes, on page 181 it tells you what units from the SM codex you can take in a grey knight army, such as land raiders, dreadnoughts, and techmarines.

Some of them have slight changes to their options and loadouts, which are listed on that page as well. For example, the Techmarine gains Psyker, psyk-out grenades, and must take a servo harness.