I have had a similar problem with my 1991 Wrangler. I found if you can pull the 4X4 stick past the 4 high the push it back up it may engage. That worked for me. The problem was ultimately fixed when I had the transmission rebuilt.
6.8 pints of 75W-90 Manual Trans Gear Lube.
80w90 gear oil
75w90 gear oil
75w90 or 80w90
your shift lever bushings are bad, easy fix.
Most likely a broken gear cluster
The transmission does not take gear oil. The auto uses ATF+4 and the manual uses manual trans fluid.
The trans does not use gear oil. The auto uses ATF+4 and the manual uses a special manual transmission lube.
75w90 gear oil75w90 gear oil
Your main bearing in the trans is going out, 4th and reverse don't use the same shaft. Get it replaced asap Note, this is common to the ax5 transmission, but is normally set off by low trans fluid.
3.31 for base differential, 3.55 for limited slip manual trans, 3.31 for limited slip auto trans
synchro second and third gear, not first gear