My 3466A was even worse than yours - none of the switches worked correctly. I surmise they tarnished from sitting around unused for decades.
What I did was to drill very small holes at the top/back of each switch. That allowed me to flood it with contact cleaner. No problems at all after that.
In my case, the 3466A wasn't a piece that I was too excited about, so the prospect of actually ruining it by drilling holes wasn't upsetting. You may
feel otherwise in your situation.