The tower was marked on older topo maps but doesn't show on the more recent maps.
The precise location is: 44.651686, -111.044661
1958 USGS TOPO (LINK)
The tower is gone, but the concrete footings are visible on the latest Google Maps imagery.
The tower was built in 1935.
The road to the lookout has long been abandoned - there's essentially no road or trail there now. The lookout burned down at some point.
The tower was around 500 feet from the main road.
This lookout has gone by several names:
Madison River Lookout
West Yellowstone Fire Lookout
Emergency Fire Lookout Station
Promontory Fire Lookout
Here's how it looked when it was still standing. Image courtesy of this fire lookout info page
1994 imagery shows the area did not appear to have burned in the large1988 fire. (courtesy Google Earth)
1994 imagery shows some sort of structure.
I'd love to get present-day photos of the site - if you head up there please take photos and send them to bavetta@gmail.com, thanks!