ThanksFor a history lesson....
Prior to dereg, the York to Scarborough route was always hourly (except winter Sundays when it was two hourly). With the 744/746 from Brid/Hull to York then Leeds, this formed the half hourly headway from York to Leeds. When joint operation ceased c.1988, EYMS took the shortened 744/6 and instead, an 844 was introduced from York to Leeds. This was operated by York depot but when Yorkshire Coastliner was carved out in its own right as a business, all 843/844 journeys were worked from Malton so that meant extending the shorts to Malton.
Contrary to @Ken H recollection, at dereg, the Malton to Whitby service was transferred to East Yorkshire (Scarborough and District) as compensation for losing its share on the Scarborough to Middlesbrough service. It consisted of an irregular service between Malton and Pickering, of which three or four went over the top to Whitby. United retained some schools journeys from Goathland to Whitby IIRC
Subsequently, this was integrated into the main Coastliner route but the section from Whitby to Pickering has kept at 3/4 journeys a day save the introduction of seasonal expresses, and that's what we see today. Rolling stock on the 843 in the late 1980s was NBC era ECW Olympians and they were later replaced by Northern Counties examples. However, 5 late model Leyland Tigers with Plaxton Paramount III bodies were bought for the 840 as it had become in 1990, and they were subsequently replaced with the last single decks being Wright Eclipses. However, ENCTS came along, pass usage went up and deckers were required and hence deckers were specified throughout.
There's probably more (and the odd error) but that's mainly how we ended up where we are today (to keep it relevant).
Trying to work out bus provision after about 1985 becomes difficult as timetable books stopped being produced and all there were were leaflets for each service.
Only later there was the internet and there is an archive of sorts on wayback machine internet archive.
So there is a 15-20 year gap in the historical document record.