Yes may be able shed some light, Mull.
The red-painted wooden post boxes were the property of the GPO and affixed to some of the single-deckers operating out of the Llandudno Town Depot. I seem to recall that even in the early 1960s they still had GVI's royal cypher on an enamelled white plate on the door but without posting times.
They used to provide a late posting facility for places on the old M11 route on its 1900 service from Eglwysbach to Llandudno. Letters and small packets could be inserted into the box by the poster at whatever bus stop on the route they signalled for the bus to stop.
I once asked a conductor who emptied the box and where - as us youngsters constantly debated whether it was at the Junction or Llandudno. The answer was that a postman met the bus on arrival at Llandudno and emptied the box (in those days there was a stop in Vaughan Street outside Lee's antique shop which would be the most convenient for the GPO).
When the single deckers were changed to one-man operation in the late 1960s or early 1970s, a new box somewhat smaller in size was provided by the driver's cab inside the vehicle. This didn't last long as, I expect, people not seeing the box on the rear assumed the facility was no longer available and use declined.
According to R C Anderson's History of Crosville Motor Services (1981), a Leyland single decker, fleet number KA27, "had a detachable post box fitted on the nearside rear panel and for years operated the Llandudno - Eglwysbach". KA27 was delivered in a batch during 1937/38. The local one was not unique as there area couple of photos in the 1987 edition of "State Owned without Tears" one showing a bus with the box visible and the other a small ceremony of a boy posting a letter in the box on the circular service in Rhyl in 1931 - said to be the first instance of such a service.