A small solar panel
works without anything else as a trickle charger. However you need to discover whether your battery is still functional. If it is then you also need to ensure that the battery charger functions correctly. A battery is one of three parts of a system. It just stores power. Something has to charge it. Then when it is time to use it ' various things will pull power back out. You mention lights, but if you have a propane furnace
it will likely have a blower fan. If the ac goes out, and it is snowing out and you are stuck in your tt, you want to know that the battery will drive the furnace
fan. Having lights isn't all that helpful if you have frozen to death
If you have a battery, then you should have a charger driven by the ac. The problem is that these built-in chargers may not correctly charge your battery. The sad fact is that they often don't and so your battery dies. Come time to use it, stuff will work for a few minutes then fail because the battery is simply dead. A trickle charger cannot charge a dead battery, it can only maintain the charge on a healthy battery.
In some circumstances a healthy battery literally keeps you alive, so get it tested. If you tried to use your battery and it didn't drive your lights you may well need a new battery.
Long term a small solar
cell like this will also not keep your battery healthy. Your battery needs to be brought to a boil, with a large charge current. The boiling causes the battery acid solution to stay mixed. If this boiling does not occur then the solution separates and the bottom of the lead plates are exposed to pure sulfuric acid causing them to become crusted with oxide and... the battery dies.
Only a real, correctly functioning charger can provide the high currents required to boil the solution. A small solar
cell like you bought will not do that.
In fact a small solar
cell may trick a cheap built in charger into thinking that the battery is fully charged, causing the charger to go directly to 'float mode' when it powers up. If the built-in charger does not cycle through the stages, and does not have a de-sulfination stage, then your battery never boils and it eventually dies.
I hate to be the bearer of bad news but you are responsible for determining that your charger actually works correctly, and if not correcting the problem. There are aftermarket chargers which will periodically bring your battery to a boil for a few minutes, which all by itself eliminates that failure mode. If your charger doesn't 'de-sulfinate' then one of these widgets is the cheapest solution.
Also remember that a solar panel
trickle charger doesn't work when covered with snow.
One thing I forgot to mention is that this does not affect AGM or gel cell batteries, which are fundamentally different from a wet cell (flooded cell) battery. These types of batteries do not need to boil to keep the solution mixed.