Hi Tim,
Monitoring the car battery current is a little harder than most measurements because the dynamics in the current levels changes wildly over various operations in the car. Still, they do make meters you can buy and install that will tell you the current level. An auto parts store might help here.
To get good monitoring of the low level currents that run things like small lights in the car, you could try sensing current yourself with some kind of current monitor chip. You'd want to monitor only the current to the accessories though, not the starting current. One glance at the readout would tell you if the current is still there or not, and remind you to shut off the lights.
Did you ever build an electronics kit and solder components?