What part should I use?

[dylar]

I want to be able to select between four contact points (only two shown in the image: A and B) so that the same LED/LDR pair can be used to control one at a time.
Basically, I want a four-position selector switch that does not make a connection, but makes it possible for a connection to be made after it.  Hope that makes sense.  I'm having trouble finding what I can use.

[anchovie]

That's still a selector switch. If the purpose is to connect A,B,C or D to the LDR there isn't really a concept of "after" or "before". A 4PST rotary switch should do the job and be easy to mount on a box/panel.