Finger-count must remain consistent.
Everybody working lights should get a pair of gloves. Even a cheap-o dollar-store pair of gloves is better than nothing. Lights can get very hot and you don’t want second-degree burns becoming a “badge of honor” on your sets. Spring for gloves.
The light structures also get hot. That includes shutters, bodies, and sometimes even the C-stands. Even if a light is off, its associated hardware will remain hot for quite a while afterward.