No ammount of rewiring the sockets will get round the fact that voltage
on the main bus drops to a few volts during cranking

This is the scheme I used for the radio and
GPS in my last but one car. The NICAD supplies the voltage when the
supply is less than 9volts and even when the main battery is removed.
The Nicad trickle charges through the 330R resistor



SUPPLY LOAD
----------|-------||--------------
/ |
\ 330Resistor |
/ |
\ |
|-------||----+
|
-------
--- 9 VOLT
------- NICAD
---
------
---
|
|
GROUND