I know you can perform a target lock on a target that is already locked to trigger various effects. Can you cloak when already cloaked to trigger the free evade action of the Stygian Particle Accelerator?

Good question. I do not know.

The answer is no. A ship cannot perform the Cloak action while it already has a cloak token.

Page 3 of the FAQ

Ah, see it now. That sucks, generic phantoms could use the bump.

Just to make sure everyone is on the same page,

A ship that already has a target lock on one ship may gain a TL on a different ship, loosing the original lock in the process. It may also gain a TL on a ship that a different allied ship has already locked, but a ship may not gain a TL on an enemy that it currently already has a lock on.