What I think I would do is to use 24 VDC relays You can use a 4PDT relay such as:
https://www.mouser.com/ProductDetail/Omron-Automation-and-Safety/MY4ZN-DC24-S The 4PDT relay likely has less current draw than two DPDT relays. So, pick the quiescent state as the stet it's likely in most often to conserve power. Multiple relays can be connected in parallel and just activated by a simple SPST switch which has constant 24 VDC power.
I'd actually put diodes across the coil close to the coil on every coil: Solenoids and relays.
The number of solenoids that the system can drive depend on the MOSFET or multiple MOSFETS can be used with the 100 ohm resistors.
DPDT might be better. You can use steering diodes to activate multiple combinations of say 4 SPST switches and they won't interact. It's called WIRE_OR.
An easy way to understand this is to put one side of the relay at +12. Whatever relays you want activated, connect a diode to those relays such that the bands are connected together and through a switch to ground. So, maybe you could have a switch with OFF.
Now it's getting down to SPST contacts when I look it over. So, you can have a SPDT switch that operates two (gizmos) One position that activates the LEFT solenoid and one that activates the right solenoid, and the other position is vice versa with center off to save power. If you used DPDT latching relays, one could be the state. This is a bit more complex to do, but it might be worth it because you can have signals. The relays latch magnetically and can be dual coil.
This post probably reads like mush and I really need to think about it. A lot doesn't make sense because I'm not 100% functional. I think better yet, you can use the dual coil latching relays on the solenoids to get position info. You may have that another way.
I didn't realize that the DPDT switch is a (ON) -OFF - (ON) switch or momentary. TRIGGER is just a label.
You still should be able to diode OR the solenoids and/or relays controlling them an any combination you want, so that multiple gismos operate at the same time. If status is not already implemented, a dual coil latching relay or micro switch could work.
Sorry that this post is so convoluted.
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In any event plug in relays and DIN real construction is the normal way to go. Terminal blocks are used for outside world connections.