I don't understand this at all. I feel like it should be a nose or ear joke. Also, I can only think of peppers when I see "Big Jim".
I researched the grower's last name. Found a picture of an old man that might have been the guy on the label. If so, then I imagine that he was known among his fellow orchardists as having a big nose, and for growing big pears. I grew some Big Jim peppers a number of years back. They were truly big and were great for hanging and drying. But the peppers were developed in 1975, so Jim the pear grower came up with the name first.
