I have a pool, and use an ancient Guardex "open" chlorinator that
takes 1-inch trichlor tablets. But I can't get parts for it
anymore, and every now and then the check valves get crud in them,
and overnight when the pump is off I lose prime. So it may be time
to get a new one.

All the modern chlorinators appear to be sealed systems. There are
input and output ports, and there's a screw-on lid that I assume is
air-tight. But I don't understand exactly how these things work.
What determines how high the water level gets inside the
chlorinator? Is there any way to adjust that? I assume it doesn't
fill up completely, but there's some air in the top.

The other issue I'm concerned about is that I only run the pump
about 12 hours a day. And I wonder what happens to the chlorinated
water in the chlorinator when I turn the pump off. Does it stay in
there and continue to dissolve the chlorine? In my old
chlorinator, the water drains out when the pump turns off, and I'd
like to keep that feature if possible.

I guess the alternative is floaters, but I'd rather avoid that if
possible.

Anyway, if anyone knows of a link where the operation of these
things is explained in detail, I would appreciate knowing about it.