A833 Noise in Third

You sure that is not an overdrive box, where physically the third gear in the box is OD; but shifting wise, the third selected gear is Direct. Each gear should register successively lower rpm on the tach, at the same speed.

Running in Direct, which you say is not noisy, should be just fine, stay out of the noisy gear, until you have a chance to inspect it. My guess is the noise originates in the roller bearings in the back of the input gear, but I'm going more by logic than by anything else. In Direct gear, the input is locked to the mainshaft and power goes straight thru the gearbox. However,
ALL the OTHER gears are still spinning, just going for a free ride.

In Direct gear, the thrust is sortof removed from the cluster, and it is allowed to bang back and forth in the box. However this fore/aft motion is usually limited to a few thousands of an inch, and you never hear it . If you hear clunking, this is where it would most likely be coming from, unless the rear mount is busted..

The A230 and the A833 are very close cousins, and for the purpose of noise discussion can be considered the same.

If you did have an od-box, that od gear is very small, 18teeth IIRC, and has no torque carrying capacity. I have broken three of them, two with a 318. They will not take any shock-loading, and IMO, they should have a lock-out device on the shifter. So yes the od gear could be noisy.

And one more;
if the M/S bearing at the back, is worn out, then the MS can move fore and aft, carrying all 3 M/S gears with it. Since the forks are held stationary by the cover, so are the synchro sliders. I have seen the M/S gears get into physical contact with the cluster, and the front-most brass pop out of the slider because the struts came out too far. When this happens, the slider cannot return to neutral, and you will be stuck in direct gear. Do not rip on the stick, it will only make things worse.
Personally I would take it out and inspect it. You only need two specialized tools; a snap-ring plier, and a notched plate to press the back bearing off so you can remove the back two gears. But if the back bearing is tight and quiet, and the gears spin nice, and you are not having any grinding issues during shifting, then there is no need to take it apart. It's a piece of cake; any grease-monkey can rebuild that trans; I was just 17 when I did my first one.