In reply to glenc: I used to get the fear a lot when I started, and have more or less got over it now.
One thing that seemed to help was spending a lot of time sitting around in the harness to get used to the idea that being that high up wasn't inherently dangerous, and turning it from something scary into something cool and exciting. So have you tried getting him to:
* climb up until he's just off the ground
* sit back on the harness (with a nice tight rope)
* dangle a bit, look at the view, wave, try to relax
* climb a few moves higher
* sit on the harness again
* dangle, look at the view, wave, relax
* repeat until actually quite a long way up
If anything this is going to be easier with a 7 year old because it'll be easier to keep the rope really tight and reassuring when he sits back onto it.
But I'd also reiterate what others have said - really don't put any pressure on him to do it. If nothing else, it won't make him feel any better about it if he thinks he's letting his dad down as well...