Alternator surging

seen your video

don't worry all OK

minor wiggle

get 1500 rpm on the tacho and switch on the lights... if it calms down life is good

your regulator provides a smooth ramp up and down of charging current for the battery
when it has switched the alternator on.....

if its switching the alternator off and on, between a state of doing something and doing nothing much, it aint that smooth and you are observing that action on your ammeter in my view.

Alternator off and on is based on RPM, demand from the cars systems, and battery charge level. a big old battery with huge cold cranking amps rating takes a lot longer to charge up. especially if it was intended for a car or truck with ECU controlled battery charging a 120 + amp alternator and a million and one electrical items installed in the car
injection, fans, heated seats and locks and steering wheel/windows/locking aircon etc.

standard alternator is just tickling that battery under the chin... :)

what was put in on the production line was the minimum viable battery, for the demands of that car in 1960-75, and what you have now even if its a no label no brand battery is at least for a period of time, years rather than months, a bigger better storer of charge with a lower internal resistance than the original.
Battery tech moved on like everything else and the charging tech in our cars aint moved since 1975.

Dave