It was directed by Barrie Osborne. I misread one of his cues, it was completely my fault, and nearly burnt the set down.

The beaconsare lit Gondor calls for aid

Yeah we actually set that on fire and Peter wanted to let it burn down. [T]hey lifted parts of that and used it for some of this beacon lighting on top of the mountain.

As noted by bob1 in the comments, the scene was filmed at Mt Gunn which is located in a National Park. New Zealand has specific laws for the setting of fires in National Parks and the crew almost certainly had to acquire permits for their fires and to ensure they did no damage to the surroundings. Lighting that many bonfire-esque pyres would've meant plenty of paperwork and increased risk dramatically.

Lightthe beacons ofgondor GIF

The day that we actually filmed the beacon actually going on fire here - that was pretty exciting because we did have a full-sized beacon which they set light to.

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Lightthe beaconsmeaning

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The beacon you're looking at here is actually built on the mountains. We helicoptered the beacon in and the little hut that these guys live in and we flew around in the helicopter and shot it being set on fire. But what you see here is real; none of this is a special effect apart from the distant beacon that lights at the very end [of the shot].

This seems to suggest not only the surprise from the visual effects supervisor that they used real fire. But also that they wouldn't leave a fire burning for a long time. The article goes on to describe how Rivers in his nervousness flubbed the first take and that the pyre had nearly entirely gone up in flames:

Lightthe beacons ofGondor

The pyre that Pippin (Billy Boyd) lights is real, which meant that the stakes of the shoot were high. Return of the King’s soup-eating Gondorian guard tells his LOTR story - Polygon

Throughout the rest of the beacon lighting sequence no other specific beacons are mentioned or highlighted as having been genuinely built, constructed or set alight (per the film's audio commentaries).

The Lighting of the Beaconssheet music

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This seemingly suggests they weren't interested in having large fires go up with people nearby. Further supporting the idea that the latter seven beacons were animated and not really lit.

According to an article on Polygon for the 15th anniversary of The Return of the King with visual effects supervisor Christian Rivers the suggestion seems to be that only the first beacon was "actually lit".

I re-watched The Return of the King, and I couldn't help but wonder whether they built the Beacons of Gondor on mountaintops and lit them to get the shots used in the movie, or at least some of them. It would strike me as quite a task to haul the logs up there, whether by vehicle or helicopter, but it also looked quite realistic. Does anyone know if they really built the beacons atop the mountains in real life, or whether they just animated the scene?