I've been thinking about a stir plate for making a batch too see how I get on. A laboratory stir plate is a device use to rotate a small plastic "stir bar" (a plastic coated magnetic bar). The idea being that a liquid substance can be stirred, without actually having something that needs to be placed in the liquid, but the liquid is rotated.
As you may know, with meads, it's currently recommended that once a batch is mixed up, it's then stirred at least once a day from the initial yeast pitch, until the 1/3rd sugar break (that's when, say, the starting gravity is 1.100 and when the yeast has burned it's way through the sugars 1/3 of the way, that is to say it's gravity is 1.066 a.k.a. the 1/3rd sugar break). The recommendation is a gotmead thing, yet it's not set in concrete, as there are some members there, who will apply aeration to a batch further, some to the 1/2 point and others until completion.
Anyway, by stirring the batch continuously, it's about getting a continuous amount of air/oxygen to the yeast, and that'd normally be associated with making starters etc.
There's also a limited amount of info about making entire batches while they're in a container that contains a stirring bar and that in turn, is placed on a magnetic stir plate.
I've had a look at places like ebay, but more often than not, the stir plate devices are too expensive, but a little hunting finds sites like this one with the instructions on how to build a home made one, using a computer fan. The only thing that needs thinking about, is whether it needs a speed controller or not. Because when a stirring arrangement like this could easily cause a vortex in the liquid, yet whether it would need to run that fast, would need a bit of experimentation, because whether it needs continuous extra air/oxygen is one question, but at the same time, it's likely to help with removing the CO2 that's produced by the yeast, and consequently, help reduce the swings in pH which can be a problem if the pH dips too low - the CO2, with a still batch, is in solution as carbonic acid (apparently), so continuous movement would help remove it by shifting it to a gaseous state.
I've also found a place that sells laboratory glassware and they have 5 litre Erlenmeyer (flat based conical) flasks, which would be big enough to make a whole 1 gallon batch (they've also got other stuff like glass beakers etc). I suspect that with a bit of effort and expense, it will be a worthwhile experiment....
Either way, I'm still thinking about it.