According to (1) blood flow maximizes around 30% of max effort. So light contractions seem best.

1: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4591373/

I'm certainly not a medical professional, but my impression is that it's not so much movement as muscle tension that helps. If the muscle just moves without encountering any resistance, it doesn't create nearly as much pressure as it does when e.g. walking. So you really need to have weight or some other sort of resistance against the motion. I try to wedge my feet against something and use my calves to lift myself off the seat.

Maybe someone who actually knows can tell me whether I'm totally off-base here?

From the article, it says that contraction of the muscles pushes against the veins. Given that, the less resistance the better. You don't need the muscles to work harder, you just need them to be maximally shortened.

In other words, what you should really do is flail around wildly. As a bonus, this also slightly increases the heartrate of nearby coworkers.

You have to flex your calves to pump the veins deep in your legs, you can do seated calf raises. Standing up and walking around is ideal.