I like the old Comets, whats going on with it, looks like a good driver.
Not sure about your car but a lot of the old dashes the switches and such are inserted from the rear of dash and the have a depth adjusting nut.
Then a bezel (chrome) nut is screw from the front of dash to lock the switch (part) in place. Normally the bezel is very thin and is removed possibly with light taping with a cloth covered screwdriver against one of the ears on the bezel nut.
I am sure they make a tool for this. I have even used channel locks.
You also maybe able to loosen the depth adjusting nut from back side of the dash so you can loosen front bezel nut by hand