Do military bases still employ wheel watchers?
No

They do not continue this practice anymore. This is likely because landing gear are more reliable now than they were in the 70's. There is also the practice of Air Traffic Control prompting military pilots to check their gear is down, by verbally adding "Check Gear Down" to their landing clearance.

Source: Checked in with some of the Air Force / Air National Guard pilots in the office. They're not aware of any such practice and decided it must have been before their time. Oldest pilot started in the 90's, so that leaves you with a 20 year gap where they abolished the practice.