Mine did that just recently, barely a drip for a while and when it went, seemed the whole bottom fell out the bucket. Last thursday's project, new pump, new T-stat and both hoses. Plus a flush and reservoir cleanout.

 

Nothing much has changed in pump tech in last 40 or so years AFAIK. It's a springloaded rotating carbon seal. If you have a dishwasher, much the same tech.
Miding the weephole is a good idea, but you'll probably see a drip-run stain. That will sometiems happen.
If it's always damp... fail is pretty much imminent.
Used to be coolant additives said something about pump bearing lubrication... Bull hockey.
Coolant should never get to the pump bearings.
Seal lube.. maybe. But there isnt any in a dishwasher, is there?!! Or you couldnt use DW detergent as a flush.