Keeping radio/stereo unit powered on, when car ignition is off?

Something is fishy here. It sounds like:

• Yellow wire labeled "battery" should have constant 12 volts, whether the car is on or off. The "bulb with a wire in the middle" is probably a fuse. (Any direct connection to the battery will normally be fused). "Memory", as you correctly guess, provides a constant power to the stereo head that retains presets etc. If you get 0v when the car is off, this is probably incorrectly hooked up to the ACC (Accessory power) instead of constant 12v.

• Red Wire labeled "ACC" should only have power when ignition is turned to ACC or car is running. If it always has 12v, then again something is not hooked up right.

Why did it not work when you switched the wires? I can't say exactly, but to directly answer the question: yes it's entirely possible for you to leave your radio on and drain the battery. However, if you really want to be able to listen to it with the car off then you would have to do something like what you have done, and splice the always on 12v to both connections on the stereo.

The only thing I might change is to make sure that always on connection has a fuse. If the line is not fused already, or there is no fuse in the panel I would suggest getting a cheap inline fuse-holder to splice into the wire. Always fuse hot connections as close as possible to the battery or other DC source.

Also if you are splicing hot connections together be aware you may be pulling more amps than was originally intended for the wire. This is exactly why you should have a fuse, otherwise the wire may heat up and melt the insulation, causing a short and/or fire.

Quite straight forward. in the stereo world the conventions are as follows: Yellow wire is permanent 12V Red is Acc (ignition switched 12V) Black is ground.

Car manufacturers quite often reverse permanent and Acc locations on ISO power plug. They also use them for different functions on later vehicles, so you may find Acc wire is replaced by CAN network connection. Earth wire is always in some position.

For your 1999 Fiat Bravo, it is probably too old to have stereo CAN bus connections ( a lot of Fiats do) You will find bullet connectors in the Yellow and Red wires - undo and swop Red to Yellow and then Yellow to Red.

As for the stereo not staying on when engine is off: This may be how Fiat intended. Check the Acc with multimeter to determine when 12v Acc is present. If not ignition switched with "hold" until key removed you will needcto locate a better switched 12v from fuse box.

Of the cars that I have personally worked on, none of them had a memory circuit that I would feel comfortable running my head unit off of; they're usually fused at 5 amps (sometimes 7.5 amps), where a head unit is usually 10 amps or more. If the manufacturer designed the circuit to handle 5 amps, you risk blowing fuses and burning wires by overloading it.

As for draining the battery, it's entirely possible, but that depends on the head unit, and how much power it draws when turned off.

If you absolutely must set yours up this way (I would not), running a wire from the battery to the head unit with a separate fuse inline is a safe bet. Your factory wiring was not designed to do what you suggest.