That button is melted into the gauge panel, so I think the only safe way is to replace entire panel. You would have to be very careful to remove it and would have to glue it in your panel. Don't know how creative you are, but the blue painters tape might be a potential temporary fix. If you have the blue tape see if light comes thru it, and try to see if it will work some how.
I just found the 66 page owners manual and the light for the hi beams is red. I guess only newer cars are blue. I put a flashlight thru it and it isn't very bright. Light is very subdued.