I tried searching, but didn't find anything. Is there a way, via a trigger, to make a non-solid brush become solid? I don't want to just enable a player clip or invisible brush around it, I want the whole thing to become solid. Can this be done? Specifically, can it be done with water?

Func_brush supports solidity toggling. As for water, there's no way to make it solid except for an invisible brush surrounding the water whose solidity is toggled back and forth.

I couldn't find solidity toggling for a func_brush, it sorta works if you enable/disable it, but it also turns invisable. Try duplicating the brush, apply invisable or playerclip to the new brush and enable/disable that one. Doing this I am able to get the effect I think you were after.

Just create your wall, make it "Never Solid".
Create another wall, just nodraw textures (so neither the player can walk through it nor physics or the Portalgun shot) and toggle this one.

Great ideas. Thanks. I will try it.

Update: Got this to work reasonably well with the invisible func_physbox. Thanks.