My mother was a Harris born in Cornwall, and it's a very common name there. Her family goes back to Gwennap and St. Allen in the 1600s, which are very close to St Agnes and Truro which you mentioned. They were major tin and copper mining areas but that all started to die out in the 19C. A lot of Cornwall miners moved elsewhere, and some would have come to the IOM.

Harris is not a Manx name. I believe it originates in France starting as "Harrie" which would be the French pronunciation of anything ending with the letters "is". Harris is very common everywhere now, but in the IOM it probably doesn't begin until the mining started.

I hope that helps a bit.