To unlock the special color-coded gates in Doom 64 map 23,
Unholy Temple:

Three gates on this level are locked and cannot be directly
unlocked with keys.  Near each gate is a rectangular marker
on the wall, which displays 3 vertical bands of color.

In the middle of one edge of the map is a rectangular room
with a central pillar.  This pillar has 3 switches on it,
colored red, yellow and blue.

These switches can be used to open those locked color-coded
gates.
The trick is that you have to Activate the colored switches
on the pillar in the same left-to-right order of the color
bands near the gate you want to open.
In other words, if a gate has a blue-red-yellow marker near
it, go to that pillar and Activate the blue, red and yellow
switches in that order, and that gate will open.

Note that if you Activate the switches in an order that
does not match any of the color markers, a monster attack
will occur.