My experience : a 13W solar panel (amorphous silicon) and my old car battery put in the trunk and used only to feed the gps, the phone charger and other misc 12V such as an USB fan.
After a few weeks I could measure 15+V while solar charging
I moved the battery from the car and looked at the water level : too low. I filled-up the battery and put it on a 220V charger. Sadly the voltage went over 14.6V in a couple minutes and the charger put the voltage on maintenance (13.6V). I let it all night long and the day after I put the battery back into the car's trunk.
After a week, the panel was always overcharging the battery and the water level was again too low. After refill, I tried to "exercise" the battery so I depleted it (an old unused 220V 40W lamp through a 12/220V converter) and charged it 3 times. Each charge was followed by a night long maintenance. charge and use phases were separated by 2 hours of rest. Each time the charge and use periods were longer.
Put back the battery in the trunk and monitored the voltage while panel charge. It was OK during a few days, but after a week it was over 15V
Then I had to use a battery for a geek project at home. It was involving higher currents (up to 8A) and the battery was used and charges through a charge controller. The battery worked very well during the 3 weeks tests.
As it was then mid-September I decided to not put back the battery and the 13W solar panel as their weight were certainly canceling the saving on alternator.
Denis.