Generally, when talking about solar and battery charging, "12v" is not an exact number. It's a range. A "12v nominal" solar panel generally puts out 15v or more. A "12v nominal" battery can range from 10.5v (dead) up to 13.5v (fully charged).
But while 13.5v is considered a full charge voltage - that's not really the whole story. "3 stage" solar controllers and smart chargers will push the battery until it gets to 14.4v (bulk stage), then drop back and hold it at 14.2v for a few hours to fully activate the chemistry in the electrolyte (absorb stage), then drop to 13.5v and say, "okay, NOW it's fully charged", and will then maintain the battery at 13.5v (float stage).
That controller you linked to, is the most simple sort of solar charge controller - it simply connects the solar panel to the battery whenever the battery gets down to 13v, and disconnects when the battery reaches 14.2v. It will get the battery "mostly" charged, but since it doesn't hold the battery at an elevated voltage long enough for the battery to fully absorb, the battery will mostly only reach around 90% charged (if that), rather than 100%.
Lead-acid batteries have what is called the "self-discharge rate". This is how much power the battery will lose if it's just sitting around. The rate is different for different batteries, and also an older battery will self-discharge at a higher rate than a newer battery.
In general, 10w or so of solar would be considered a "maintainer" - i.e., it's too small to do anything other than put out roughly what is needed to compensate for the self-discharge of a battery that is just sitting.
To know if 12w of solar would be enough to maintain the battery, you would need to know how much the battery self-discharges, plus how much parasitic load is on the battery, such as a car alarm, the clock in the radio and whatnot. If that totals up to more than 12w, then the solar panel would be fighting a losing battle. Since the solar panel wouldn't provide enough to ever get the battery up to 14.2v, the charge controller would just basically be leaving the panel connected to the battery all the time.
In that case, there would be no need for the controller. 5w and 10w solar battery "maintainers" usually DON'T use a controller since they are too small to ever overcharge a big ol' lead-acid battery. The main purpose of a charge controller, is to prevent overcharging. Connecting a 100w panel to a battery could easily overcharge it if there was no controller to disconnect the solar when the battery was full, but a 1a (12w/12v=1a) charge isn't enough to hurt anything even if it was left connected all day.
(That is, for a battery in a vehicle which is actually being used, and the occasional use of the solar panel. For even a 12w panel hooked up constantly to a battery (such as are used in a lot of electric gate systems), I WOULD want a charge controller, since in that situation, it would be "theoretically" possible to overcharge the battery even with a dinky little 1a charger.)
The next question is: Will that solar panel you linked to put out a high enough voltage to get the job done?
The solar panel has to put out a higher voltage than whatever it is charging (plus a little extra to overcome a sort of "electrical inertia"), that is why "12v nominal" solar panels that are intended to charge a "12v nominal" battery are setup to put out 15v or more.
The specs on the page you linked to seem a bit vague. Solar panels have all sorts of rating numbers, and the only thing that page says is "Max output: 12 watts (12volts / 800mA)". If that panel actually does put out 12v...well that's not enough to push a battery up to 14.2v, or even 13v.
Now, the first thing I notice is that the math ain't right. Watts / volts = amps.
12w / 12v = 1a
Not .8a.
However, if we do it like this:
12w /
15v = .8a
Okay, that works out. So my
guess is that the panel is actually a "12v nominal", which actually puts out 15v. If so, then it could be used to charge a "12v nominal" battery.
The number we really need, is the "Vmp" (voltage at max power). That is the voltage that the solar panel is capable of under full load. A few minutes of Googling doesn't turn up the user manual, but I do find this on the Brunton support page:
http://www.bruntonoutdoor.com/support.php?category=Portable+Power (last question)
"Q. When I check the voltage of my panel with a volt meter I am getting 19 to 22 volts. I thought it was a 12 volt panel?
A. This is normal. You will find on an open circuit, when there is no load or device hooked to the panel, your voltage will read that high. Once a device is connected or the panel is loaded, the circuit is closed and your panels
[sic] voltage will register at the expected 12 to 15 volt range."
So...if the Voc (voltage open circuit - i.e., no load) is 19v-22v, then the Vmp is likely to be in the 15v range.
Thus, that is a "12v nominal" solar panel, not a "12v" solar panel.
Which WOULD work to maintain a "12v nominal" battery.
But I would say you probably don't need the charge controller for a such a dinky little solar panel connected to a big ol' lead-acid auto battery.
In any case - even if it does put out 15v Vmp (I would want to confirm that for sure before I hooked it up), don't expect it to do much more than compensate for self-discharge + small parasitic load. It's just too small to do much more than that.
1 amp just ain't much in the "12v nominal" auto/marine battery world.
