'Normal' mode is actually the protocol for the 'Konami Justifier' on PS1. Also, seemingly, the Justifier was cross compatable with the Saturn using an adaptor. It's possible that with a Saturn adaptor of some sort, the gun would work on a Saturn.
The Justifier predated the Guncon, it doesn't require the video pass through adaptor to be connected, the justifier gets it's video sync data over the controller cable somehow. I also have noticed that the Justifier based games seem less accurate, but this was done using third party Hip Gear guns, I've never seen a first party Justifier for PS1.
This is a guess, but I think the decrease in accuracy comes from the PS1 itself processing and doing the math between it's vidoe sync rate and when the gun see's the CRT beam. In the Guncon and Guncon2 design, dedicated circuitry inside the gun does the math and just spits out X/Y info to the PlayStation. Personally, I prefer Namco's offical Guncon 1's, my favorite console gun, best shape and best look.
A third party however, is probably the best for a cab, cause you can switch modes on a whim and play either Justifier, Guncon or Guncon 2 games without difficulty. Though I find that Namco's models for PS1 and PS2 are more durable and well built.
