To read up on leadership duties, I can also thoroughly recommend ShackTac's strategy and gameplay guide (or any of Dsylecxi's stuff, for that matter) which should be freely available on their website. The complete guide, adding special weapons and tactics, was bundled with Arma 3 Deluxe. Check if you have that, then use it. It's a good read, too.
Is there any chance for some kind of leadership workshop? Have a show-and-tell dry run with a whole squad and then take turns to ascend to TL and eventually SL. Being able to show off having completed that workshop might encourage people to fill TL in a live mission, or at the very least be confident enough to assume command when the former lead is KIA.
I'd volunteer to hold the class, preferably with someone else.