What does it mean if my Watchdog backup sump is flashing "Add Distilled Water" even with brand new battery?
The unit in question has two large current-carrying wires which connect to the positive and negative terminals of the battery, and a sense wire which is designed to connect to a probe supplied with batteries manufactured by the same company.  The probe is a thin metal rod that sticks through a special hole in the top of the battery; the hole is placed so as to ensure that the rod does not touch the plates in the battery (having a metal rod touch the plates could be spectacularly bad, so this feature should only be used on batteries that are designed for it), but the tip of the probe will sit in the acid solution; the acid is a good enough conductor that if it reaches the height of the probe it will effectively connect the probe to one of the battery terminals.  If the charging box doesn't see that connection, it will flag a warning.

Note that a 12V battery consists of six independent two-volt batteries, each of which must be serviced separately.  The probe only senses the level in one of the batteries, but if the batteries are all filled to the same level, they will generally lose water at the same rate.  It would have been helpful IMHO if the unit had included probes for all six batteries and provided a means of reading their status, so as to make it easier to fill the batteries uniformly (otherwise it's hard to judge the fluid levels in them), but perhaps some other means of viewing fluid levels could have been usable.

In any case, I have a pump by that manufacturer and it worked successfully even through a 36-hour power outage coupled with heavy rain, so I'm pretty happy with it.