As far as I know, Mercedes used the same gearbox in multiple vehicles, just like they did with the engines - the OM352A turbodiesel engine from the 1300 and 1500 (and the OM366A from the "xx00 turbo" models) were used in lots of different vehicles including Merc's own lorries, etc, and I believe also in other manufacturer's vehicles from around the world, so the same is probably true of gearboxes.
Honestly, I know very little about Unimogs so I can't offer much advice or info on them.
By the way, any official Mercedes dealership should be able to talk to you about parts if you give them a chassis number for any Merc machine, including the MB tracs. It would be best to talk to a big/old dealership where there might be some staff who actually remember the MB tracs, or maybe find a dealership that sells a lot of trucks if you want to talk to someone in the parts department that could give you general info on engines and gearboxes, for example if you wanted to know what engines/gearboxes could be transferred between machines and so on.
There's an interesting old video on Youtube where a guy swapped the engine out of an MB trac that he bought as a non-runner for a good engine out of a Merc lorry here:
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The way you described the gear-changes above sounds about right, although it's quite hard to describe in written form!
The MB trac my brother owns is a 1985 1300 model (although it got an engine upgrade to the later 366 engine and has around 170hp - the engine was taken from a Merc 1617 truck) and it has this gearbox. When starting, only gears 1-4 are available for selection in the basic H-shaped layout with 1 at the top left and 3 at the top right. In order to be able to select 5 or 6, you need to swing the stick to the far right while in neutral, at which point you can usually hear the little gush of air as the 'gate' is opened, which then allows the stick to move into 5 or 6. You follow the same procedure to access the 7 and 8 gate.
You have to operate in the same way in order to move from the higher gears back down to the lower gears. So you can't go directly from gear 1/2 or 3/4 to 7/8 (or vice versa), you need to access 5/6 first and only then can you also access 7/8.
I hope that explains it reasonably well...
By the way, there is a green light that operates at the base of the stick (and to the rear of the stick) that lights up showing the pair of numbers that are currently accessible to you at any given time, so that helps when you're not sure what 'gate' you're in or if you're having difficulty selecting the gear you want. Obviously, this light may not be working in these old tractors but it is invaluable when first getting used to the tractor once you have one, or if you're trying to test-drive one.
I found a pic on the internet, seems to be from a 1500, that shows the gear levers and hydraulic controls and even shows the green light on for gears 3-4.
The hydraulic control levers are in the middle of the pic and the PTO and other gear levers are to the right. For the benefit of anyone who may not be familiar with the symbols for those levers, the bottom one in the pic is the PTO speed selector; the next one is the selector for front PTO, rear PTO or both**; the next lever is for the high and low gear ranges; and finally the fourth lever at the top is for a crawler box which I think was only an option on the MB tracs, so it is usually not present as is the case in this pic.
**The front PTO was optional I think, and is not present on all MB tracs.
By the way, there's a guy on farmingforum.co.uk (username 'Rs chunk') who was looking for a big MB a year or more ago who eventually got a real nice one late last year, a 1988 "1300 turbo" with the longer bonnet & vertical grille, etc. It was his first MB trac, so he would have gone through the learning phase by now and could probably offer you some good advice on getting used to them. You could create an account on that forum and contact him that way or send me a private message with your email address if you want me to email it to him.
You can see the thread where I first talked to him about the MBs (not unlike this thread!) here:
Mb trac
Also, one final thing - there is a tidy 1500 model for sale in the adjacent county to me, just across the border in Northern Ireland. You can see it here:
https://www.donedeal.ie/tractors-for-sale/mb-trac-1500-tractor/14245004
He's looking £18,500 for it at the moment; sounds a bit dear to me but maybe he'll drop the price a bit for a serious buyer. I saw the tractor once, but it was a good few years ago now. It looked really well at the time and he wasn't afraid to use it on long distance trips so it must have been running well. My brother bought a silage wagon from a dealer who lived about 50 miles away from us and he got this guy to collect the wagon and deliver it to us with his MB trac. (This was a year or so before we got our own MB).