The NES and the 2600 do NOT use the same switchbox. The NES uses an automated switch, like modern systems do, based on RF. The 2600 (and all systems pretty much prior to NES) use a manual switchbox. You can't use the same one on both.
What you can use, however, for the 2600 is this:
That little adapter can be had at Radio Shack or similar for a couple of bucks and will dramatically improve the picture over what your 25 year old switchbox could provide.
For the NES, best use is the RCA jacks that are on the console itself. I know, most people ignore them, but they are there to be used.