at pin X605-2, but the only way to prevent it to dry out the battery, is to turn it on only when the head unit is turned on, so X606-9 acts as a turn on signal. This is a white wire that also feeds power to the antenna amplifier.
I would check at the back of the head unit, at the 16 pin black connector (X18126), with the plug connected, that this white wire in position 16 is getting 12 Vdc when power is turned on. If there is the proper voltage, check continuity for this white wire to the amplifier end. A simple check you could perform is to connect power from X605-2 to X606-9. Amplifier should turn on and sound should reach the speakers. Be extremely careful of connecting the right terminals. It is the white wire the one that should receive 12 Vdc.
If head unit is not feeding 12Vdc when turned on to the white wire, you may want to check the head unit socket for corroded, bent or missing pin, or open it looking for a broken internal line feeding this 16 pin connection.
Javier