I would get a multi meter and check the voltage coming into the battery when those spikes are present. If the voltage regulator is actually kicking out and letting it "run wild" for those couple of seconds then its a faulty regulator.
If the regulator sticks open and produces too much power, the battery could explode.
'87 YJ, 4.2L built and bored, 8.5" of lift, 8.8 rear, AX15/NP 231, Tom Woods drive shafts, Flat fenders, 12,000LB winch, Custom bumpers, Rattle can paint job. Never completed...