Back in 1986 it was the 06:00 Glasgow Central - Ayr, forming the 07:40 Ayr - London Euston, 09:10 ex Glasgow Central. There were special instructions in place that related to the neutral section at the south end of Newton-on-Ayr station, in that it was feared that a loco hauled train calling at Newton-on-Ayr would be unable to gain sufficient momentum to get through the neutral section, and would end up gapped. So there was no Newton-on-Ayr stop scheduled on the 06:00 Glasgow Central - Ayr. If for any reason the loco hauled set was swapped to another diagram (e.g. 06:30 Glasgow - Ayr) then a "Not to Stop" order had to be issued for Newton-on-Ayr, and passengers directed to the following service.
It was nearly always an 86/2, but it did get an occasional 87 or a roarer (81 or 85).
The last daytime loco-hauled Euston - Glasgow service I travelled on was late December 2004, so that confirms route101's dates.