It has a Freedom 25 Charger/Inverter, controlled by a Link 2000.

When I turn off the charger using the button on the Link, the charger
only stays off for a few minutes. When the fully charged battery drops
to about 13.6v, the charger switches back on. It's subtle, because the
"charge", "accept" and "float" lights and the "charge" light do not
light. If you're not watching the voltmeter, you won't notice.

Is this the way it's supposed to work? The manuals imply that this is
the default option that can be overridden by DIP switches on a manual
control panel that I think the Link replaced.

The only way I can shut down the charging is to kill the 110 to the
Heart. Unfortunately there is no separate breaker on that line.
ANSWER:
When the link 2000 is connected to the Freedom 25 all control over the
invertor is through the link. Refer to the link manual to set the many
functions of the invertor/charger. There are more than 15 functions
that can be set from the link if you want to monitor and protect your
investment. If your link does not have the advanced battery
temperature function set the charge voltage range based on the average
battery box temperature. Once the functions are set the charger can
be left on to maintain the batteries at full charge and unlike most
other chargers the voltage will remain at float state when small loads
are applied. Because this charger can produce over 100 amps I
recommend the power sharing function be set for low output, most boats
can get buy with a 25 amp. charger.

From the author of books on boat refrigeration
http://www.Kollmann-marine.com