Firebeacon was a convalecent home in Cove, Tiverton. It was run by Mrs. Unwin, wife of the local J.P.
It might be the same home mentioned in the 1890 Charities Register as Mrs. Unwin's Incurable Home, Haynes, Tiverton. This was established in 1888 for "the reception of destitute girls, between the ages of 4 and 12" who had a chronic illness. Admission was free, but a medical certificate was required "together with a statement as to the pecuniary position of the parents." It had room for 8 permanent beds.
As the Unwins seem to have been rich philanthropists, I would assume they had connections in the large towns and cities who would recommend children from poor families to be sent there.