Hello Creamtea, for some reason, there is a marked absence of festivities celebrating Virgens on the west coast of Tenerife in October. Where the Virgens go in October remains a mystery.
For October, the Santiago del Teide Council website only lists the Fiesta in honour of la Virgen del Pilar, Las Manchas (north of Arguayo) on October 12th with no further detail.
However, if you have a hire car and care to travel further a-field, on October 3rd (or thereabouts) there are the Our Lady of the Rosary celebrations in Fasnia, El Rosario, Valle War.
On 1st Sunday in October the Pilgrimage of Our Lady of the Incarnation, Adeje.
On 15th to 20th October Festival of Christ in El Calvario and St. Ursula.
And last but not least, 21st to 25th October (or thereabouts) the annual festival of Our Lady of Hope, Virgen de los Remedios and St. Bartholomew in La Guancha, Buenavista del Nort in honour of the town's patron. This is claimed to be a week long series of events, celebrations and processions, fireworks, music, sport, drinking and dancing.
But check these dates out with the tourist board when you arrive because the only thing I can absolutely guarantee on any of these dates is the drinking.