Re SB-SFO in post #48 the classic 747 APU battery was in the unpressurised tailcone area just in front of the APU firewall. It sat on a heating pad to stop it from freezing and, inside a box with a fan to cool it in high ambient temperatures. The 744 had the APU battery in the closet as you state.
Copy of classic AMM 24-30-00--"The main battery and the APU battery are nickel cadmium and are identical and interchangeable. The main battery is located on the floor behind the flight engineer's instrument panel. It receives power from a charger located on the E10 rack (Fig. 1). The charger input is from the ground service transfer bus which is powered from ac bus No. 1, APU gen 1, or external power No. 1. The APU battery is located in the tail section
between the aft pressurized bulkhead and the APU firewall. The APU battery receives its power from a charger located in the E13 rack".