Figured I might as well make this topic since it's bound to come up.
If you can't mount the twon-ha after buying it it's because your PCs processor is too fast. I came upon the same problem a few years back and found that running a CPU-throttling program works. Basically launch something like CPUkiller before launching the game and you should be able to ride the little bugger.
http://www.cpukiller.com/

I thought GOG always fixed these games to automatically adjust for things like this? I mean if we have to use 3rd party programs to compensate... then what exactly are we paying for?

The GOG version does in fact fix this, at least according to this post: http://www.gog.com/en/forum/outcast/cd_audio/10

Yeah, are you sure GOG didn't fix this already?

Well my CPU is pretty bad by modern standards, a core2duo at 1800MHz. Hope it works for everyone else!

The twon ha getting stuck in the swamp is not the bug I'm talking about. With certain processors it simply will not work and as far as I know the solution I mentioned is the only fix.
If GoG has worked it out then great.

I have a hard time thinking this bug hasn't been fixed. I mean, that's the purpose of GOG :)

The context-sensitive action icon on the upper right-hand corner of the screen should also change to the appropriate "mount Twon-Ha" icon when you do it right.
Are you sure you are trying to get up on the right Twon-Ha? It should be the one in the pen in the center of the village.
By the way, a rather unrelated question: What happens when your Twon-Ha dies? Is it gone for good, or can you get a new one at some point?

There are at least three opportunities to get a Twon-Ha. But I would really suggest to get the Twon-Ha early on in Shamazaar, because that's the region where it is most useful.

There's only one Twon-Ha that it would make sense to mount since all but one are carrying riss around. My context-sensitive action icon is in the left-hand top corner of the screen, and it doesn't change from jump when i move around the twon-ha with gui in my left hand.

Yea, i'm getting the same issue, can't mount it because the icon never changes. Have the bought gui, am in the middle of the village with the single twon-ha in the pen, but nothing comes up... annoying.

My bad, the icon is in the upper left-hand corner, of course.
You've actually said that you have the bought gui in your hand, but just to be sure: Apart from the gui you get when you buy the Twon-Ha, you can find another one lying around somewhere and you will get one during a quest. You specifically have to equip the gui that you bought to be able to mount the Twon-Ha.
Though, that probably isn't the issue. Have you tried slowing down your CPU as suggested in the opening post of this thread?
The only other thing I could think of is loading an older savegame and buying the Twon-Ha again, just in case the game somehow didn't recognize the purchase.

Pen in the middle of the village? Maybe my memory is failing me, but the twon-ha I bought was located in a separate pen within walking distance of the village, towards the portal that takes you to Talanzaar.
Not to say this is the problem you're having, but make certain you're trying to mount the twon-ha that corresponds to your gui. I say this because I remember thinking the same thing... turns out I was simply trying to mount the wrong one.