First of all, I think “When…Charge? And When stop?”
Normally we should charge battery when voltage lower than 12.4 volts and voltage maximum of most battery is 14.4volts but someone guru tell me voltage saving of 13.8 or 13-volts approximately.
Secondly,Thus we need to use comparator circuit which in first times I often use IC-op-amp such as LM339,LM311,LM324,LM301 but sometimes we cannot buy them. And This our working is simple stye only.
When begin we learn basic principle of electronic parts, I like use Diode, Zener diode, which they are both valves for electrical currents. The Current will flow one way. But the zener diode is connected backwards. It then blocks current until the voltage exceeds a certain level.
I try to test them with the zener diode 12-volts the current will flow through it when voltage higher than 12V.
Therefore I use Zener diode for detects voltage over than 13V to control stop charger system.
Then, I use relay to control current to a battery. Because cheap and used easily.
Next, I use a SCR for uses as quick control switch.