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I don't know that these are anything special other than 'long red peppers', but wanted to check. They have a thin skin and what I'd call a sweet taste, though not as sweet as a bell pepper. Theres very very subtle heat. Like a notion of maybe spicy.

My grandma (Italian, if that helps ) had these growing in her yard, and I saved some seeds to plant this season. She passed away over the winter and the house was sold, so I don't really have any way to track it down.

Check this out. It is close to your description of a thin walled Italian pepper with a square end.

https://www.rareseeds.com/melrose/