In the nocash doc it lists the 10 resolutions possible on the PSX GPU. Framebuffer section quite near the top.
H: 256, 512, 320, 640, 368
V: 240 or 480
(368 having a horizontal frequency of 7.603200MHz)
The “bit” (1, not 0) that activates 368 mode is nothing of concern IMHO. Imagine it like a dip switch, for 368 it needs to be on (1 ) and for all other horizontal modes it needs to be off (0).
A little lower down it also mentions dot clocks, where Namco GunCon chip has a slightly higher frequency of exactly 8.0MHz and scans 385 horizontal pixels.
This implies that an emulator whose GPU code isn’t absolutely accurate could produce different horizontal scan line widths. To get 384 horizontal width, the frequency would be 7.933774MHz.
I would say 384 is a mistake that has propagated.