Whilst not entirely within the OP timescales, I worked in Glasgow Control in the mid 80s and confirm that class 31s were very rare in Glasgow Central at that time - and I believe that was also the case in the period enquired about.
I only ever saw one class 31 at Glasgow Central, and that was in 1984 when the numerically unusual 31101 worked in on a parcels train, and was sent straight back south on the 22:xx parcels to Nottingham (1M65?). It was that unusual that I delayed my journey home to get a few photos of it.
Class 31 did work into Edinburgh Waverley from the Newcastle direction from time to time, whenever the Eastern Region were short of power and had nothing better to offer. By chance the heaviest southbound overnight was the 2230 Edinburgh - Kings Cross (1E39) and that was booked for Gateshead traincrew, so if there was ever anything that only they could drive - such as a class 31 or 37 - it ended up on that train. I had a 31 on it once - on load 14 it was 105' late by York!
I think the train to Glasgow formed of Sealink stock was the 0120 (SO) Stranraer - Blackpool. A circuit of Sealink stock worked Glasgow Central - Stranraer - Blackpool - Stranraer - Glasgow Central. (In previous years this had been an out-and-back working from the Blackpool end, northbound on a Friday evening and returning south at 01:20 Saturday). The direct Glasgow - Blackpool may also have been Sealink stock - I don't recall.
The Glasgow - Morecambe was notable for being diesel hauled throughout, and also for doing the direct line Hest Bank - Bare Lane i.e. not via Lancaster.