Do military bases still employ wheel watchers? When I was in the air wing in the '70s, I had the unpleasant opportunity of pulling wheel watch. The unfortunate individual sat in a small shack (maybe 3 x 6 ft.) with a pair of high-powered binoculars ensuring that each and every aircraft on final had their gears down. If not, there were two flare guns pointed at opposite right angles to the runway that had to be fired to warn the pilot off. I know I had to use them on more than one occasion. I think it was a thirty-day hitch. It seems like such a primitive way to ensure the gears were down, and I wonder if it's still being used today?
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.