This sounds like one of two problems. I have had a few batteries over the years do this. What happens is the battery keeps taking in the amps but the battery voltage level wont go up as high as it should. In other words the regulator will keep charging the battery (putting amps into it) until the battery reaches the set voltage level to cut the regulator back (field circuit) back to drop the charging amps into the battery. The set voltage of the reg may be 14.2 and if the battery will not rise to that it will take in amps all day long as the reg will keep the field circuit energized and keep it charging the battery since the reg thinks the battery is still low. The only way to verify this is to put a good battery in it and see if it fixes it.

The other deal is that its just charging full output all the time as the older Mopar alternators dont put out enough at idle to push the amp gauge all the way past center but if its got full field all the time (full charging) it will make the amp gauge show more amps the more you step on the gas. It could be a wire shorted that keeps it at full charge and which wire depends on if you have the single or dual field alt.
Your best bet is put an ampmeter and a voltmeter on the car and test to see what the readings are. The best test ampmeter is the kind where you unhook the output wire on the alt and hook the ampmeter in series and then hook a voltmeter across the battery. Then start the car with everything off and see what the meters read as you bring the rpm up. If the amps keep going up and the volts do not then its either a low battery or a bad battery. If the amps and volts keep climbing then its over charging for some reason which would need to be diagnosed. Ron