I'm having a bit of difficulty understanding this 1964 timetable, could someone have a look please - I'm looking for a suitable gap in traffic from say 12.30pm to around 3pm on Saturdays only in the Beverley area?
This might sound counter-intuitive, but I'd start with the Bridlington times, because everything calls there, then look at the Beverley times for the stopping trains to Hull.
The stopping trains depart Bridlington at 10.55am, 11.52am, 12.45pm and 1.41pm, roughly intervals of 55 minutes. Each of these call at Beverley, and, except for the slower 1.41pm, take about 30 minutes to get to Beverley.
Now look at what departs Bridlington between 10.55am and 11.52am: there are long distance departures from Bridlington at 11.5am, 11.14am, 11.25am and 11.42am, so we know they can fit in at least 4 other trains in a 55 minute gap between local trains, possibly 5 if something can run between 11.25am and 11.42am.
The gap between the 11.52am and 12.45pm local trains has Bridlington departures at 12.19pm, 12.27pm and 12.37pm, so there is a gap for 1 or 2 trains to depart Bridlington between 11.52am and 12.19pm (say at 12noon and 12.10pm) passing Beverley about 30 minutes later.
The gap between the 12.45pm and 1.41pm local trains has Bridlington departures at 1.4pm and 1.27pm, so there is a gap between 12.45pm and 1.4pm (say at 12.55pm), a gap between 1.4pm and 1.27pm (say at 1.15pm), and possibly also a gap between 1.27pm and 1.41pm (say at 1.35pm), given that the 1.41pm gets further behind when it stops at some of the smaller stations before Driffield.