Here are a few more screen shots from a couple little videos I shot when overhauling my unit (mine is from a 69 with AC, but basically the same).
Note that the positioning of the selector left/right slider lever will affect reach to this bulb as the 2 pics show. The bulb is a 1445 bulb (same as the one in your transmission indicator) I replaced mine with a BA9S single pole cool white LED from hipo parts (3rd pic shows what that looks like now). The bulb socket is a friction fit inside a metal hole in the switch assembly.
It will be hard to get to (if not damn near impossible.. :-/) but you might have a shot at wiggling it free with your arm up in there and your hand on or near the socket and its wire. Note that there is a metal clip to hold the wire for the light on the drivers side of the assembly (you can see it on the edge of the metal plate in the pics. It just slides on, but I'd recommend removing it before you try to get the socket out, as it restricts the socket movement by restricting the wire movement. If you can get the socket free, stick in the other bulb, pull the headlight switch at least halfway out (so the bulb should be ON) and touch the metal bulb socket to metal (ground) to make sure it lights up. Once the new bulb is sure to work, guide the socket back to its housing and if you get it in the right position, and and give it a good push, it might go into the hole to stay.
I'd say you have a remote chance at getting it replaced without removing anything, but if you remove the radio, I think you are good. my radio was out when I put mine back and I swapped the bulb while in the dash rather easily in that config.
Good luck! Post pics if you can! it helps lots of folks!
Jay