When I disable the visuals on the Assimilated Shield, the effect keeps coming back at times. Normally when turning in a battle, it just fades back into view then vanishes again.

Kind of annoying and confusing because I like the shield but not having a Borg ship; what's the point of disabling (or using) it if it won't disable?

What you're seeing is the Borg set procs, the Autonomous Regeneration Sequencer and Multi-Regenerative Shield Array, which only last several seconds. They proc when you're under fire, regardless of whether or not you have the visuals disabled.

Edit: The Autonomous Regenerative Sequencer proc is when parts of your hull glow/flash green, which is probably what you're referring to.

The Multi-Regenerative Shield Array proc is when the actual shield bubble glows/flashes green.

Just got the repair one and it was, never saw it happen together before... and it's the exact same effect I disabled, so disabling it's still pointless.

Sigh. You disabled the visuals of the equipment. Not of the effects of the equipment.