Following issues in the past with self-verified times and an inconsistent approach to timing, You do not need to show any timer on screen as I will always double-check runs.

For Mayhem Mode, run time starts when you press X to select your first character.

Time ends when "Player Victory" has appeared on the screen. Note that you can hold X at the end of a run to speed this up a little:

For Strategy Mode, run time starts when you press X on the final pre-amble screen before loading Crater Lake:

Time ends when "Teknos/Arcane Victory!" has appeared on the screen. Note that you can hold X at the end of a run to speed this up a little:

For extra clarity, runs using an emulator are fine so long as it is a PS1 ONE emulator. Do not submit runs if they were performed using a PS2/3 emulator since it is known that PSX games loading times are often much quicker on later PS systems.

Be aware that RNG for map movements in Strategy Mode will sometimes change depending on how a previous map or fight played out. That is, if you practice a Map in isolation, you may get a different enemy movement in an actual run. RNG for enemy movements seems to be related to your health following battles, and will also change depending on your precise hex movements. I have not yet encountered any possible manipulation of this RNG relating to starting a new run in Crater Lake after doing another map and quitting, and if you find a way to alter enemy movements in Crater Lake by this method, please let me know. It would be best if all runs started from the same RNG for now.

I have added difficulty as a variable so that the boards are far easier to navigate and 1st place runs are properly marked, thanks to AlrightSally for pointing that out to me.