Just beat me to it David. In June 1985 the Permanent Way Institution held its annual summer convention in Portrush. One of the excursions that delegates could go on was to Dublin where they visited the CTC Centre and an exhibition of permanent way equipment in what is now the car park at Connolly. The PWI delegates travelled in the MkIIIs from Portrush to Lisburn as a special train (not sure what hauled it - could have been the CIÉ loco which had worked the empty stock from Dublin to Portrush). At Lisburn the MkIIIs were attached to the rear of the 09:00 ex-Belfast for the journey to Dublin. As far as I remembered the delegates returned to Belfast and on to Portrush on regular trains and the CIÉ stock did not go back north.
Anthony, the original video is wrongly dated December 1984 and is in fact a compilation of cine films taken by Barry Pickup over a number of years. JHB, unlike the times when Cravens were attached to the back of a MkIId set and were locked off, there was no problem running NIR MkIIs and CIÉ MkIIIs together as the brakes, couplers and gangways were compatible. Railer, the MkIIIs were at the back of the train because it was more straight forward to do it that way in Lisburn. To put the MkIIIs at the front of the train would have required a lot more shunting, with resulting delays to the 09:00 service. I reckon that the photo linked to in David's earlier post (# 7) was the trial trip for the June special and would have operated without passengers in any part of the train.