The bottom line with the minor German states, or the Third Germany if you wish, was that they had to contend, Holy Roman Empire or no, with the continuous possibility of encroachment of both Prussia and Austria on their territory and independence. And that is why in 1805 Wurttemberg, Bavaria, Hesse-Darmstadt, and Baden chose to ally themselves with France, as the lesser of two evils, and were enthusiastic about the Confederation of the Rhine being formed in the summer of 1806.

Hanover was a British possession and Brunswick a British ally, with Hesse-Cassel being closely associated with Great Britain at least as far back as 1745 when Great Britain hired German mercenaries to fight the Jacobites in Scotland. And that is why Napoleon both occupied them and then formed them, or parts of them, into Westphalia. Those three states were never part of the Confederation singly and only became part of it when they were formed into Westphalia.

And Hamburg was never part of the Confederation either. The only member of the Confederation that was annexed after belonging to the Confederation was Oldenberg.

The member states were:

Bavaria
Wurttemberg
Baden
Hesse-Darmstadt
Grand Duchy of Frankfurt
Berg
Nassau
Saxony
Saxe-Gotha-Allenberg
Saxe-Meiningen
Saxe-Weimar
Saxe-Hilburghausen
Saxe-Colberg-Saalfeld
Grand Duchy of Wurzberg
Westphalia
Anhalt and Lippe (five principalities)
Schwarzenberg, Waldeck, Reuss (four principalities)
Oldenberg
Mecklemburg-Strelitz
Mecklemberg-Schwerin

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