The following trains appear to have been regularly steam-hauled (but not necessarily every day) right though the year of 1962.
DOWN 7.45am Plymouth to Penzance passenger
4.20pm Truro to Penzance passenger
UP mid afternoon Penzance to ????????? parcels
5.50pm Penzance to Truro passenger
6.00pm Penzance to London milk train
I am sure there would have been a few others, particularly freight trains.
I travelled down on the 7.45am from Plymouth (11.50pm ex Paddington) on 3 November 1962 and the train was pulled by a Hall class 4-6-0; although I believe it was sometimes a Castle. The loco returned on the mid afternoon parcels. I saw the 4.20pm Truro to Penzance and that had a Hall that day. I saw a steam hauled up freight at Liskeard on my journey down in the morning.
Hope this helps. Regards, Mike
So I was watching out for it!