We really need a photo of the tree to help you. Good pruning takes some skill and finesse and advice can't just be dished out sight unseen.

A picture is really needed so we know what you're dealing with. If a redbud has sufficient space to grow naturally it shouldn't need much pruning at all.

as to proper pruning time.. we need to know where you are.. big city name... ken

we prune to achieve a goal.. not just for no reason ...

limbing up a tree is common and is no problem .. topping is NEVER approved ... imo.. if it doesnt fit.. get rid of it..

we do NOT cut stuff off the top.. 'topping' is never recommended .... in the hope to fill out the canopy.. think about that ... time alone will solve the canopy issues.. tree time i counted in decades.. so just give it time..

if one insists on topping a tree.. it is not because it is good for the tree ...

we do prune out all damaged parts .. because that IS GOOD for the tree ...

ken