Here's a picture of my water pump that I restored about 15 years ago. After doing a vinegar rust removal treatment, I decided to take the pump apart to add the seal at the rear of the rear bushing. My pump never leaked a drop in the 10 years I've run it, but the seal will better keep the grease out of the coolant and the coolant out of the grease. A rebuilt original pump is the most trouble free and leakproof pump I know of.
This picture also shows the thermostat I added 5 years ago, and the drier nylon sock I just added after the vinegar treatment, to make sure any loose rust can't plug the raidator tubes.
BTW, when I grease the rear bushing I will unscrew the brass nut, so the grease can push out the front, rather than push against the seal.