My experience has been that Mexican air security people in Cozumel do not allow any batteries in carry-on unless the batteries are installed in a device. No loose batteries. This applies (depending on time of day, mood of security person, skill of security person, moon phase, tidal conditions, weather and other mysterious factors) to virtually every kind of battery you might carry. If they find a battery in your carry-on, they are likely to tell you to check it (not possible at that point) or they will seize it.
This poses a problem if you use lithium batteries, because the TSA will not allow loose lithium batteries in checked luggage in the USA. If they find them they will seize them. Many of us have to catch connecting flights within the USA while enroute to and from Mexico and the batteries are likely to be found.
If you have more lithium batteries than you can install in devices, then you have a problem. Bear in mind that Lithium batteries include things like Eneloops which are kind of expensive, and many rechargeable proprietary batteries for lights, cameras, etc., that tend to be very expensive.
If you have a battery-operated device in which you are willing to leave lithium batteries installed, then that solves the problem, but if you want to take extra proprietary camera batteries that often cost $30.00 to $60.00 a pop, that can be challenging.
There are creative solutions to the problem, such as taking extra flashlights with you solely as battery containers or relying more on alkalines in devices where they can be used, but the bottom line is don't plan on taking loose lithium batteries out of Cozumel unless you are prepared for them to get taken.
A Sola light should be no problem no matter how you carry it.
I have actually found that if you leave a lithium camera battery in the charger, there is at least a chance that the Cozumel security folks will consider it to be installed in a device.