Remember when the 737 was certified. Digged out my old -300 manual and it says:
The standby horizon indicator provides attitude information that is independent of the primary attitude displays. The indicator is powered by the battery bus and remains powered after the loss of all normal AC power as long as battery power is available. The gyro reaches operational speed approximately 60 seconds after power is applied. The indicator requires three minutes to achieve accuracy requirements.
The following list identifies the significant equipment that operates when the battery is the only source of electrical power and is powering the standby busses.
Flight Instruments
• clocks (hot battery bus)
• standby airspeed/altitude indicator
• standby horizon indicator
No individual battery pack i'm afraid, that's something only the ISFD has on the 737 series, 150 minutes battery power as said above. You gonna notice when the battery is gone anyway as the display blanks.