They look like the tools we used to make for removing the pointer from pressure gauges, could also be a watchmakers tool for pulling clock hands from a taper shaft.
The one on the right looks like a hand jack for pulling the hands off pressure gauges. The point on the screw looks buggered. The one on the left is a clamp for wire on some type of electrical equipment.
Definitely a pointer puller for pressure gauges or clock hands. Used one almost every day to pull pressure gauge pointers off for calibration. Check out the link here.**LINK**
The one on the left looks to be the clamp section of an earth tag. The earthing strip is slipped through the groove, wrapped around a copper water pipe or ground stake and passed through the groove again then the screw tightens it all up.
I made a similar gadget to the one on the right for pulling the pinions from stepper motor shafts on telescope mounts.
Thjere are similar fittings to the brass one on the church lightning conductor.