Hmmmmm sounds a bit weird.
So you are saying that If the Stereo works, then the fuel pump has some issues,
and if the deck doesnt work, then the Fuel pump is 100%
Doesnt quite sound like the Alternator or Battery to me as well.
It could be the Battery regulator, but from what I have heard with regulators, if they blow, then the Car Voltage can jump up to 15-16V, not actually be limited to around 10V
Then again I could be mistaken ?
Id say that you have some sort of intermittant High Resistance short or something, that when the wiring is playing up, it is chewing some very high amps, but not enuf to blow fuses or anything like that.
Are there fuses for Fuel Pump, deck, etc, and are these blowing at all ???
Does the problem seem like it happens with physical movement (Bumps, etc)
Is the problem intermittant, can you make it happen all the time, or is it a freaky type problem ?
Other things to check is grounding on chassis, and the connectors on the Battery, Alternator, and Regulator, as if the Ground (Chassis) is not 100%, or any of these connectors are rusty or dodgy, then you can have symptoms similar to above
Im not 100% sure though ???