The path he was on came to a dead end. He was trying to find a way to go forward.
Unfortunately, because of the bad set design, you need to look extremely closely to see that it's a dead end. Watching it casually, it looks like the Doctor was trying to climb down the cliff, and halfway down realised what a bloody stupid thing to do it was. But if you look carerfully, the "balcony" he was on doesn't lead anywhere. It is (just) possible to see that—but it needed to be obvious and it wasn't.
This has been commented on in interviews with various people involved in making the story. "Dragonfire" is due to be released on DVD on 7th May 2012 (in the UK), as part of the "Ace Adventures" boxed set, so it's quite likely to be (certainly ought to be) mentioned in the commentary and/or other DVD extras.
There is said to have been a scene deleted (because of lack of time) from the broadcast story that explained why he did it. This is something else that may become clearer when the DVD is released.
Supposedly, the writer (Ian Briggs) told fans they'd have to read the novelisation for an explanation. If you read that novelisation (also by Ian Briggs), there isn't any bizarre mystery about the Doctor hanging from his umbrella for no reason that jumps out at you, but it doesn't really directly explain the TV version, either.