Commander Kinsey wrote

How does a lead acid battery charger (or car alternator) know when to
switch to trickle charge?

From the current the battery takes.

I can understand it noticing a drop in charging current if the battery is
on its own, but what if a random changing load is connected, as there is
in a running car?

You just look at the current going to the battery. The variably
loads like with lights isnt supplied by the battery when the
engine is running, its supplied by the alternator.