The Billings Radio Construction Company looks to have been the manufacturing arm of Wyn Billings Radio Ltd. (given that the 'Bellbird' brand was sold by Wyn Billings**).
As a side note, Wyn Billings Radio was a separate company to Preston Billings - Wyn and Preston were brothers. A third brother, Cliff Billings, ran the production line at Radio Corporation of New Zealand.
Originally they were located at 3 or 6* Cornhill St (possibly the old premises of W. Marks Ltd / Radio Corp NZ who moved from Cornhill St to Courtenay Place at this time?), then from around 1941 they were at 8 Herbert St (sometimes noted as the corner of Herbert and Edward Sts, City).
* The Cornhill St location is shown as 3 on one of their chassis badges, and 6 in newspaper advertising - so they might have moved? Or one might be in error.
** The original Bluebird sets are believed to have been made for them by Radio Corporation (NZ) Ltd, c. 1933 - thereafter they bore no resemblance to RCNZ sets
EVENING POST, 16 OCTOBER 1936