And father Rafael, with his impassive, ageless face and his ancient cloth-making skills, certainly looks as though he would have been at home in the Peguche of another era.
While we watch, he dexterously cards a tangle of wool - these days mostly from sheep rather than vicuna or llama - into a strip of fibres. Then, using a hand-operated spinning wheel powered by a giant wooden flywheel, he transforms that into a coarse thread.
Finally, and most remarkably, he demonstrates the working of the ancient backstrap loom to transform the thread into a tightly woven strip of cloth.
This involves one end of the loom being tied to a post or tree and the other to a belt round the weaver's waist; the back muscles being used to pull the warp threads tight, while the weft threads are moved back and forth by hand.
It has the advantage, points out Cesar, of being portable; able to be used in the market while running a stall, in the square while chatting with friends or in the yard while watching the children.
But, he adds, the stress on the back muscles is considerable. "Even a strong man like my father can only use it for four hours a day."
The backstrap loom is also limited to producing fairly narrow strips of cloth, so for anything broader the Cotacachis use what they call the Spanish loom, which has only been in South America for 450 years or so.
These days, they also incorporate a range of cultural influences in their designs. "That one," said Cesar, pointing to a brightly coloured wall-hanging, "is Navajo from North America."
I wanted to buy something with a traditional Quichua design and he pointed across the studio to a wall-hanging worked mainly in browns and blacks. "That is the only one we have. It is a dancer. It was made on the Spanish loom."
A wall-hanging produced on the backstrap loom, Cesar said, would take perhaps 12 days to make. The one I was looking at had taken only three days to weave on the more efficient Spanish loom. The price I paid for it equated to about 90 minutes' work back in New Zealand. I think it's remarkable.
Rafael didn't demonstrate the workings of the Spanish loom, which I suspect was a bit newfangled for his tastes, but at another studio in Peguche a female weaver, Luzmila Ruiz, showed us how that operates.
First she used an even more primitive spinning technique, involving what I think is called a drop-spinner, to transform wool into thread by hand. Then she used the loom to weave some of that thread into a few centimetres of cloth.
Even more intriguingly, Luzmila also took what looked like a white fungal infection on a cactus pot plant - but was actually a female scale insect - and rubbed it on to her palm to create a purple stain. Then she added lemon juice, which turned it crimson.
This was cochineal, a dye used by the Mayan and Aztec civilisations to colour their cloth for hundreds of years, which created a sensation when it was exported to Europe following the Spanish conquest. These days, of course, it has been displaced by artificial dyes, so it was extraordinary to see it still being used.
There are, in fact, many traditional crafts still being practised by the people of these mountain villages. Further down the Andes chain, at the village of San Bartolome, we watched the Uyaguari family produce a variety of stringed instruments by hand.
One brother was carving the base of a traditional charango - a bit like a mandolin - out of a block of wood. Another used a chisel with incredible precision to create an inlay on the body of a guitar. And oldest brother Santiago was moulding an armadillo shell into the shape needed to use it as a sounding box.
This created some consternation among members of our group, but Santiago was quick to explain. "We don't hunt the armadillo to use its shell. But the natives eat it so there are always shells around. If we can get the shell of one that is already dead, it is okay for us to use it."
A great place to see the crafts produced by the people of the Andes region is the craft market in the city of Otavalo. This is very tourist-oriented and Carlos, our guide, warned that we needed to check that items were actually made locally and not cranked out in distant factories.
Nonetheless, it does bring together an extraordinary variety of goods and most clearly are made by the artisans of the mountain villages. I spent a happy hour wandering round admiring the musical instruments: guitars and charangoes, panflutes of every size imaginable - which the vendors play between sales - and the small drums used to accompany dances.
Then there were wooden toys, clay finger puppets, paintings, jewellery made from the silver still mined locally, carvings, panama hats, ceramics, carved nuts and all kinds of leatherwork.
Mostly, though, the market specialises in fabrics - the ponchos, embroidered blouses, headbands and belts still worn by the indigenous people of the area - not to mention a vast array of scarves, gloves, jerseys, rugs, tapestries and, of course, wall-hangings ... though none, I was happy to note, as good as the one I had bought from Rafael Cotacachi.
CHECKLIST
Getting there: LAN Airlines flies daily from Auckland to Santiago with onward connections to Quito or Guayaquil in Ecuador.
Getting around: World Journeys offers an 8-day Haciendas and History package visiting Quito, the Otavalo markets, rural craft villages, Cuicocha Lake and Cotopaxi National Park. Price includes hacienda and other 5-star accommodation, transport, sightseeing and entrance fees with local English-speaking guides and most meals. Airfares are additional. Phone 0800 11 73 11.
Further information: To find out more about visiting Ecuador visit ecuador.travel.
Jim Eagles visited Ecuador with help from Lan Airlines and World Journeys.
