Alternator Gauge Reading High With 300 Watt Stereo System Installed---1969 Electrical System

Well I'm not sure calling it an "added source" is accurate. The only source of "juice" is the alternator. Unless you add a battery charger and plug it into the grid, heehee.
But the capacitor can smooth out the power delivery between times when the sound material is not sucking electrons like a newly born baby on it's mothers breast.
But then, the battery should be able to do that job, on a 300 watt system.
Even banging out bass, the amp is only gonna put out it's max for say 50% of the time cuz bass is not a continuous draw but a pulsed draw. So even tho the amp may be required to put out 300 from one peak to the next, it may in fact only be pulling 1/10 of that between the pulses. Then you add the rest of the signals and maybe the amp only puts out an average of say 30 watts say, for the sake of argument. Ok and say the amp is just a typical 10% efficiency. That means even tho it is blasting out 300 from time to time, it is actually pulling more like 30/.10=300 from the alternator on a somewhat continuous basis. Ok so 300 watts at 13 volts say,is 23 amps. Badaboom!
And that old 69 alt is probably a 35 amp job. So even with the ignition running and the 69 headlights on, you still have a couple of amps to spare. A couple.
Here's the thing, If you pull all these amps thru the factory electro-mechanical regulator and the 35A alt, neither of them is gonna be excited to be doing that for long periods of time. Sooner or later the reg is gonna fry the points closed and put the alt into maximum overdrive, which is gonna have the battery boiling it's electrolyte awayin no time, and then it is toast. The alt., now having no shut-off is brazenly going to keep on pumping electrons, and they have to go somewhere. The alt. is just a big old electron pump now. So round and round they go and on every trip the wires get hotter and hotter, and hotter. Maybe you get lucky and the alt. fries itself first. Maybe you're not so lucky and the bulkhead connector catches fire first.

Ok so, the preventive maintenance is to get a bigger alt. that is capable of running like this, and switching over the regulation duties to the electronic type regulator, and running a big old cable straight to the battery to shunt this hi-current around all the factory wiring, and finally, install a big ol'battery that can take some abuse.
Of course with the bypass now installed, the Ammeter is ignorant of that so it kindof goes on vacation. You will need a different way of monitoring the system status.
Or you can install a big ol' relay on that shunt-wire, and trigger it from the ignition circuit.
Since the stereo will draw an average of maybe 23 amps, plus the regular load of lighting and ignition, the total might be right about 35A, and she is running 100%. To get your duty-cycle down to a more sane 50%, you might want to run a 70A alt, and that might take a different electronic reg than the stock 71 up type system. So research that. And then you will need two or three more things; 1) upgraded wiring throughout the system,from the battery thru the ignition sw, and to the stereo, and 2) probably a higher idle or a different set of pulleys, and 3) an on-board fire-extinguisher.

Ok that's my 2 cents.