IIRC, the NMT runs north up the ECML through Newcastle at about 12:15 on a Saturday, and returns south sometime on Monday.
I've always found that Tuesdays and (I think) Wednesdays are the best days for freight at Tyne Yard. The Lindsey to Jarrow oil tanks arrive in the yard at about 14:00-14:30, where it crosses the southbound Jarrow to Lindsey empty tanks which arrive at about 14:30-15:00. These trains are usually formed of 28 TEA bogie tank wagons and are class 60 hauled. The loaded tanks are then tripped to Jarrow from Tyne Yard in two fourteen wagon portions, due to a limit on the number of TEAs Jarrow oil terminal can handle at once and still allow the loco to run round.
The Redcar to Hardendale lime empties, formed of PAA and PGA cement hoppers, arrive in the yard after 15:00 and can be hauled by a 60 or a 66 depending on the loadings. In "the good old days" this train used to load to 44 wagons, but the last few years have often seen the train length substantially reduced.
The North Blyth to Tyne Yard alumina tanks from the Alcan works arrive at around 13:00, formed of 12-14 PCA four wheel tank wagons and hauled by a 66 which runs round and heads back north light engine immediately after dropping off the wagons in one of the two unelectrified staging sidings.
There are also periodic MGR coal trains, run by DB Schenker, Freightliner and GBRf. Freightliner Heavy Haul and GBRf coal trains do not stop at Tyne Yard, but just pass by on the main line. Only northbound GBRf coal trains, bound for Tyne Dock, run up the ECML and pass Tyne Yard, the southbound trains from Tyne Dock to Drax run via the Durham Coast. I don't know whether it is still the case, but there used to be a northbound Heavy Haul MGR working past Tyne Yard at about midday. The majority, but not all, of the DB Schenker MGR workings call in at Tyne Yard rather than just passing by.