Question

I'm thinking about building a aeroponic setup but have 1 main big question. Do the sprayers/misters run 24/7 or do the need to be set on a timer?

Use a recycle timer. One minute on three off.

If you do go with a cycle timer make shure you get a good one! One that comes to mind is titan, the insides are made
By solid state and are good quality! The reason I bring this up is if it fails to turn on your plants will die soon

I'd suggest sentinel or whatever the other guy said.

CAP's are probably the best price but you get what you pay for!
And if you buy online, just know it'll take at least 2 weeks to get anything turned around and sent back from them.

you can run it 24/7 but its more nft than areo an you need airation in rez. i would get a cycle timer like 1 min on 5 min off, al b fuct uses on like that but overall get one that is within 3-5 min off an 1 min on.titan makes a good one as well as c.a.p