I think it depends on the surface. If it's impossible to climb, they fall. If it requires a check, they have to make one or fall. If it doesn't normally require a check, they just stay up there.
Of course, and I've always been an inveterate house-ruler. But since we are discussing GURPS and not everyone reading might be familiar with the rules I thought it might be useful to point it out. I might have been less assertive, though.
What do you think about paladins? From reading them, it seems to me that they are less powerful, but more versatile. However, I've not yet played with the 2024 rules.
I'm currently playing in a 5e 2014 campaign which should end in a couple of months or so. I'm also playing in an AD&D play-by-email which has been running since 2007 and is still going strong.