One of the hallmarks of the bridge on the original Enterprise was the view screen with a strip of blinking lights underneath it. I don’t know if anyone really knows what those lights were supposed to do, or even if they have a specific name—they just pulsed in perfect time, like some kind of Starfleet metronome. This design/technology was carried forward on ships for a century or more, all the way up to the Enterprise-E.
More recently we saw evidence that this design even predates Kirk’s era. In the series Enterprise, the NX-01 has it’s own strip of blinking lights below the main view screen. But we have to look back even farther to approach the origin of these blinkies.
The next time you watch First Contact, look at the overhead console in Zefram Chocrane’s warp ship. Although he doesn’t have a view screen as such, his cockpit was outfitted with a small strip of these blinking lights.
So, from Cochrane’s day forward the ubiquitous blinking view screen lights have been as strongly embedded in starship design as the twin nacelle warp drive. This suggests two theories: either they perform some specific, vital function common to ships across the centuries, or they have been retained as an homage to Chocrane and his historic flight. (Which is ironic because in artistic terms it's probably the other way around - his lights were likely an homage to all the "future" ships we've known all along.)
On the other hand, like the NSEA Protector’s digital conveyor in Galaxy Quest, they may just be Christmas lights, boldly blinking where no one has blinked before . . .