I think this applies to more than the sniping case. If an enemy locks onto your last know position and you peep out, he/she will have the advantage. So even if you don't move, at least look out from a different position. If you're detected by the oracle though, move for sure (saved my life a couple times).
Moving is only required when you're playing without communication to your team. Usually they can cover you or warn you to move if you're currently being flanked.
Alternatively, stay in one spot on purpose with your cloak ready to go and purposefully lure people to your position. Open up on them with your pistol from a location slightly behind where you were sniping from.
I would agree to this to a certain point. If you notice you're spotted by another recon, move immediately. The thing is though is that if you're getting kills from that spot, don't move for like 10-20 seconds because moving makes it so you can't support your team from enemies because you're not killing. I agree with moving spot to spot, but I think you should pace yourself or your team may end up dieing.
I'm going to be making a Recon tip thread too It's going to be way bigger and more in-depth than anyone could possibly want it to be! and i'm going to keep adding to it until i get bored! yay! I'm definately going to make sure to include the thoughts represented here in it, though. It's something I hadn't payed much mind to in how I play. Thanks, guys