Syncro rings have absolutely nothing to do with gear popouts. If your gears don't grind when you try to shift, they are working correctly.
There are 3 things that can be amiss here. Two are easy fixes, one is not.
By far the easiest thing to fix is a sloppy shifter. They have two welds on them that break, a couple small o-rings that wear out, and a pair of roll pins in the tranny top wear out, and start to back out. These all reduce the amount of gear engagement you get when you try to shift it into different gears due to the amount of slop they introduce into the system.
You can check on these by taking your shifter boot off, then grabbing the little "ball" that sticks up out of the top of the transmission (while it is in neutral!) pushing it in, and turning it counter-clockwise. It should then pop up and out. You can then grab the shifter, and pull it right out of the transmission.
Take a look at the bottom of it. You should see the welds on the round part with the little slots in it. If you see any cracks in either of the welds, they need to be re-welded back together.
Now, this next part varies depending on the shifter, but some of the older ones had an o-ring in them to help with spacing. It will probally be worn down to be flush with the tip of the shifter (which shouldn't be worn down BTW). Mine was a newer one, and had a solid injected bushing for the whole thing, and didn't use any o-rings. It did have the cracked welds however.
Next, take a look at the little roll pins. Make sure that they are all the way in the hole. If one is broken in half, or backed out, then get some hose clamp to hold them in after you re-install the shifter.
Second easy possiblity is worn shift forks. They have a nylon / or teflon coating on them that wears out with time, and will cause the gear not to get proper engagment. To check them, you'll need to remove the top of the tranny. If you've got a removeable hump, this should be a relatively straight forward job. First, put your shifter back in, then put the truck about half way into reverse. This lines up the reverse shift fork to slide out without hitting any gears on the way up. Undo the bolts that hold the top on, then using the shifter as a handle, lift it straight up. You'll understand immedately how the tranny works after you get the top off. Check the tips of the forks to see if there is any coating left on them. If it is down to the bare metal (check the low gear fork, since it doesn't get used much, it usually has most of the coating left) then you'll need to replace the forks. They can be bought new, but they are not cheap.
Last thing, is that your countershaft's snap rings are loose / broken, and are allowing the gears down there to walk forwards or backwards. To fix that, you need to remove the mainshaft, then the countershaft, and put a steel sleeve inbetween to replace the snap rings, and prevent the gears from moving around.
Hopefully it is just shift forks, a broken roll pin or something. If not, best of luck to you :S I can imagine getting a 200 lb tranny shipped to the middle east will not be cheap!
)..other than that,I'd say start using first and third,and skip second gear if possible..
Gotta put the shifter back in, and stick it about 1/2 way into reverse though.
