Thanks everyone. Research on items like this relating to carriages is often a work in progress. Today, I accidentally came across an article on "roundabout trains" dating to November 1902 in Railway Magazine. This has a different slant on the trains running to Tynemouth from Newcastle Central and New Bridge Street stations, which were sited a ten-minute walk apart in the city. "The majority of trains travel from Central via Heaton, Wallsend and Percy Main to North Shields, Tynemouth, Whitley Bay and Monkseaton, and thence via Backworth and Gosforth to New Bridge Street; but a few use the Riverside line from Central to North Shields. The New Bridge Street to Monkseaton section is not by any means a busy line at present and there are only a few Blyth and Morpeth trains in addition to the Tynemouth "roundabouts", the latter of which run approximately hourly. But the other section is a very busy one, there being many trains between Central and Monkseaton, for Tynemouth, Cullercoats, Whitley Bay and Monkseaton provide residences for a large proportion of the business men of Newcastle, besides which there are favourite seaside resorts in the district."
The article went on to list 13 trains from Central to New Bridge Street: - 7.00 7.13 8.50 9.55* 10.27^ a.m. 1.05 2.00 3.50 5.10 6.20 7.05 8.17 9.22 p.m.
From New Bridge Street to Central: - 6.55 8.23 8.48** 9.53** 10.38^ a.m. 12.35^ 2.03 3.08 4.58 5.10^^ 5.40 6,48^ 8.18 9.38 p.m.
(* Semifast between Manors & N. Shields. ** Fast between Manors & N. Shields ^ Via Riverside line ^^ All Stattions Saturdays, other days **).
So, in 1902 it seems to be that most sets ran between Newcastle Central and Monkseaton, with only thirteen going all the way to New Bridge Street via Monkseaton and then back to Central. In my opinion, I think that it is at least possible that those 13 trains each way were not Gould coupling equipped. Perhaps the four seven-car sets I mentioned earlier. This would leave the nine Gould coupling equipped seven-carriage sets running in the busiest section, from Central to Monkseaton via Heaton, Wallsend, North Shields, Tynemouth and Whitley Bay.
The article also mentioned that work was under way extending track from New Bridge Street to Manors. Evidently it took over six years to complete the works. Another snippet within the article was calling the N.E.R. the "king of relief trains", with some Saturdays seeing local passenger trains not just duplicated or triplicated but sometimes quadrupled or even, in extreme cases, quintipled! To be able to quadruple or quintiple services must have drawn heavily on older stock in the carriage sidings. I imagine that it also put enormous strain on passenger locomotive resources too. This provides "cover" for turning out an older or rare locomotive with potentially six (or even four) wheeled carriages. 1902 possibly saw some of the latter in the sidings. At that date there are likely to have been many older carriages which had brakes but no heating equipment (what joy on a relief service prior to Christmas).