I didn't know any Early Bronco came with a 60a alternator, but perhaps that's what they meant when the sticker said "heavy duty alternator" maybe.
What year is your Bronco? It's entirely possible that it came with a 40a model when new, and certainly possible that when someone changed out a bad old alternator they put in a low output model to save money.
There were 40, 45, 50 and 55 amp models back then, and maybe even 60 but I always thought the 60's were aftermarket upgrades as the manufacturers and rebuilders started putting more and more high-output parts in their units.
Either way, there's no way to know about yours anymore, without testing it.
It could have been an up-rated rebuild where the rebuilder did not re-stamp the housing. It could also be very tired and not quite capable of putting out it's original 40a output.
While you're this far in, you might as well take it in to your favorite local parts store that has someone that knows how to use the test equipment. Or if you don't have one of those, perhaps an auto-electric shop nearby?
Even though the heater blower motor itself is not too much for the alternator, when you start adding things like headlights, engine running, hazard flashers and radio working, a 40 is definitely working at a deficit.
If yours tests out weak, it's time for at least a 60 or 65 amp model as a direct replacement without changing any wires.
As I'm sure you've seen here, you can also up-size to the original large-case 1G for 70a or 105a outputs, or just jump right to a 3G model with internal regulator and go with a 95 or 130 amp model.
Or look for a stock replacement that's been uprated to 100a or so that will bolt right on.
Lots of choices, but any one of those with more than 70 or 80 amps output, or with a different case design, is going to require some additional wiring on your part.
Paul