Well technically a Nov. 1976 FJ40 IS a 1977 model... so YES it will work.
That being said Emissions stuff is about the only real difference between the two. It really depends on if your harness, or the 1977 harness, is a California spec, or a Federal Spec harness. The California spec harness will have a lot more Emissions stuff.
Everything else is pretty much identical as far as switches and lights go.