Disagree. Then there would be no 4L either. Assuming there IS good 4L with ADD and T/c both engaged. You should confirm this first of all. Drive 50 feet in a curve and you will feel it.
Most likely is 4H detection switch on the TC or it's wiring. Relatively easy fix. This happened to me when somebody effed up a clutch job and broke the connector on the 4H detection switch.
Only sure test is by-pass the switch and see if it engages ADD. You should first confirm TC engages. Front propeller shaft aka drive shaft should turn by hand in 2wd, and then lock up with 4H engaged and engine off (no vacuum for ADD). Then start engine and bypass switch. Drive car a little to feel if 4H truly engaged. On asphalt, slow speed, you will know right away as it will bind on any curve and 4wd light will come on.
You can get to the connector through the shift hole or access the wiring at the ADD relay in the right hand kick panel. In either case, ground the blue wire. (The above assumes 5-speed '97 J-shift same as my '99 5-speed J-shift. I think it is.)
I really don't think it can be anything else if 4L truly works. Detection switch is the only difference in the circuit between 4H and 4L.