1969 Ford 250

Having problems eliminating what might be wrong with the truck. Stick shift, v8 has a 390 engine. I believe that the slternator was going out and therefore replace the alternator. When unplugging the battery the truck automatically turns off regularly if I unplug a battery the car does not turn off, I am unfamiliar with the older models need help eliminating what I might have to replace or what else to look for in order to replace. I dont want to drive it long distance because if the battery dies then will need to be towed. What other parts should look at in order to make sure they are running well.