There may be another wire that rubbed thru and shorted to ground somewhere,that can cause the pulsing--usually a wire that isn't fused,like the headlamps or main feed to the alternator's stud on the back..
Whatever killed your fusible link may have damaged one or more of the three diodes in the alternator's diode trio,which is usually included when you buy a new voltage regulator..
The alternator will still charge as long as at least one diode is working,but at reduced capacity--if you have an idiot light for the alternator instead of a volt or amp meter,it will usually glow dimly at night with the headlights on and other electrical loads like the heater,etc...also when the vehicle is shut off,the battery can discharge to ground thru the defective diode,but this does not always happen.
I believe the diodes and the rectifier bridge in the alternator are what converts the three phase AC voltage it makes into DC current,and if the two of those items get damaged it can cause this pulsating action..
I've not bothered trying to test a diode trio,cant tell you how either,I suppose with a multi-meter you can check to see if the diodes only pass current in one direction,but I'm not sure how to test a "trio" of them,just individual ones on other things I've messed with..
A garage that has a ocilliscope might be able to tell if the alternator is causing the pulsating..
You must take the alternator case apart to get at the regulator and diode trio,it's not that difficult if you have some skills doing such things,if not,a salvage yard alternator is cheaper than a new or rebuilt one..