According to the UK Army Roll of Honour, 2985450 Private Joseph Wyllie of the Argyll & Sutherland Highlanders died on the 19th October 1939. I have been unable to find this man commemorated on the Commonwealth War Graves Commission website, however, and so the only additional information I can add at this point in time is that he was born in Glasgow and was living there when he enlisted.
At the going down of the sun, and in the morning, WE WILL REMEMBER THEM.
Ancestry (UK Army Roll of Honour 1939-1945)
The Commonwealth War Graves Commission