I have been using a livewell for...well...decades.
The normal rule of thumb for me has been to turn the pump on and off periodically to keep the water freshened. This works fine in freshwater to keep warmwater fish like bass and pike alive for example. I don't like running a livewell if I'm working a shoreline, for example, as I think the noise of the motor turns fish off. And I don't like tunning the pump while underway because the intake for the livewell is in the stern of the boat and while the boat is underway the pump is sucking nothing but air. So my interval is as I'm idling toward a spot to fish, or as I'm about to take off to go to a different spot. I did take about an inch off the top of the overflow tube to keep the water level just a bit lower and prevent sloshing on deck in choppy water.
That said, I also use the livewell in saltwater to keep bait alive such as mullet and bunker. My experience with this started out dangerously for the bait as the livewell could handle only a few at a time due to high oxygenation requirements. If I'd get a castnet full and dump it into the livewell, the baits would expire pretty quickly. The solution was two part: 1) to add yet another machine - a recirculating livewell oxygenator that forcefully lifts the water from the bottom of the livewell and sprays it over the top creating lots of bubbles. Worked great, but the technical issue with this was that the filter mechanism would clog up with scales if there were too many baits in the well. and 2) putting fewer baits in the livewell and focusing on quality amd friskiness! I know some people also inject oxygen from a tank into their baitwells to perk up the bait, but I've never done that.
The recirculator also works well when you pull the boat up on the trailer to go home. If you keep it going it will keep the fish alive so when you go to clean them they will be fresh (alive) and not dead, waterlogged and punky!
Ohhh. Another thing. Be sure you keep a screen on top of the overflow tube when using the livewell for bait. Nothing like a dead finger mullet (or other life form small enough to get sucked into it) jamming up your overflow tube. Don't ask me how I know that one....
So my perspective on this depends on the situation.
Hope this helps.