Reel Repair by Alan Tani

I'm pretty sure you are correct. Many Penn reels are convertible with simply a sleeve, star, gears, and maybe an eccentric. I think the Long Beach, Del Mar, Jigmaster, etc.

There are a few that require the side plates for location of the dog and spring, like the 180 (and I think most Surfmasters - I don't have one to verify). The dog and spring are attached/set into the side plate vice attached to the bridge. This is part of what makes them so fiddly to reassemble, haha.

Now, I only have a handful of Penn reels for examples, and much of my info is derived from scouring threads here or mystic parts diagrams/parts lists, so take that with a grain of salt.  Seems like there are very few "absolutes" with Penn, haha.

The Jigmaster I received very well may be a conversion, but Mystic Parts does not specify a unique left hand side plate required for conversion. That said, the free spool lever does sit forward of center, but I don't think this will be a problem in use.

There was a time when Penn used a sticker on the side plate to indicate it was a left hand reel - so some lefty reels out there are missing a LH sticker and do not have it molded in with the model number.