Ion channels don't exhibit any firing patterns: neurons exhibit firing patterns that depend on all the channels present [...].
I understand it this way: The observable and measureable firing pattern1 of the neuron (created at the trigger zone) is the linear superposition of tiny "firing patterns2" of all the (voltage-gated) ion channels at the trigger zone, which in turn depend on the probabilities of opening and closing which are the same for all ion channels of the same type and obey some Hodgkin–Huxley-like law. These probabilities correspond directly to the shape of firing pattern1.
The rhythm with which each single sodium channel opens and closes ("firing pattern2") doesn't have to mimick firing pattern1 exactly, only roughly and probabilistically: the open-close-ticks must occur near to the spikes of firing pattern1, but not exactly and not at every spike. And some complete outliers are allowed. The rest is superposition.
Seeing things this way, indiviudual ion channels do exhibit "firing patterns2", but these may look quite different than firing pattern1 (although not completely).
Is this kind of reasoning correct?
If so: Can the following conclusion be drawn: The time scale of a firing pattern1 depends on the number of ion channels at the trigger zone? This might be seen when looking at the rise time of a single action potential: If there is only one sodium channel, rise time will be larger, if there are many, it will be smaller. Is this correlation strictly linear?