The weep hole’s there for a reason—it lets coolant or water leak out when the seals inside the pump are shot. If you block it, you’re just asking for more trouble since it can build up pressure and mess up the pump even more.
When mine started leaking, I knew it was time to swap it out. Honestly, whether it’s for your car or something like a garden or irrigation setup, having a pump that works properly is a must. If you’re in the same boat and need a garden water pump, I’d say check out https://tecnotools.com.au/collections/garden-water-pumps. Makes life easier when they ship fast and back their stuff with a warranty.