Connecting pc's to arcade monitors can be tricky.
There are basically 3 different states.
First, there is the bios starting up. Older pc's indeed used a 640x480 during that state.
More modern pc's however might figure out the native resolution of the connected primary screen and use that.
A pc vga monitor has a small iic eeprom chip that contains data about the supported resolutions.
Arcade monitors don't have these as they don't assume that other systems will be connected to the monitor.
That's also the reason why most adjustments are just done with potmeters. Pc monitors check the video resolution and
digitally adjust things like image position and width to previous memorised setup.
In a second state on the pc, you have the os starting up. In linux, you have clearly separated bootloader. In windows, you will see a splash screen. Depending upon the version of windows, it will or will not show you some animation during that phase.
In a third state, the dedicated video driver for the video card is loaded and started. It should now jump to the resolution that was selected in the operating system. If modern windows see a PnP monitor (that is sending it's working resolutions using edid), it will only allow the selection of the resolutions that the monitor support, excluding those that the videocard can't handle. If I remember well, you can override this behavour in windows.
There isn't much you can do about the resolution of state one (the bios). I remember seeing small pcb's with the eeprom that could be placed between an arcade monitor and a pc so that the pc can query the monitor.
State 2 might be adjustable. Google is your friend to figure this out. You can customise the splash screen as well. It's not an easy proces. Embedded Setups can be a source of information, as they run into the same problems.
State 3 should be easiest to adjust, but you can again run into problems if the pc can't query the monitor it's supported resolutions.
A tft monitor can be helpfull diagnosing resolutions as most have a setting to temporary show the new resolution on screen when it changes.
Some modern tft monitors don't support 640x480 anymore and it's a troublesome resolution to use, as all system windows don't fit anymore on the screen. Windows xp assumed you wouldn't use anything smaller than 800x600.
Sorry if this post is a bit off topic. Might fit better in the monitor/Video section.
Racing cabinets often have arcade monitors with a maximum 640x480 resolution, so it might be helpfull here as well.