On the other side I just finished the Chapter in Founders at Work on 37 Signals. David Heinemeier Hansson created BaseCamp and he only spent 10 hours a week on it. He was the only programmer working on it too. Designers did help out but they only gave a third of their time too. But he said this lack of time was the greatest gift to the development of Basecamp. It helped focus his view on what they needed, and it forced them to make tough decisions about making less software all the time. When you have a lot of time you just get tempted to try to do it all, or at least do too much. So maybe if you don't try to do everything and just the essential then it might be a gift too.
37 Signals embraced the constraints that were forced upon them.
So the short answer to your question is . . . it depends. But it's still a question that needs to be asked.
Based on my experience I can say that, persistence is what matters. If you work full-time and are not persistent or loose focus then you are not going anywhere. If you work part-time and are persistent and focussed then you will win. May be it will take more time than usual but you will get there with better results.
So I would say, yes go ahead and work part-time on your idea, but be very persistent to spend whatever extra time you find on the idea. It would be good idea to find group of friends who can work part-time with you. (I did that it does help a lot)
Any recommendations on especially pertinent fields? I'm planning to look at SOA type stuff - intelligent agents, evolutionary algorithms, systems architecture, etc. I'd like to throw some Godel in there too, but can't really see the applicability yet.
If you have to look for something to do or ask for recommendations, you'll probably never have the passion needed to see it through.
OTOH, you probably already have what you need. What really bugs you? And others you know? When's the last time you said, "You know, someone really ought to make <some thing>." THAT'S what you should be pursuing.
In answer to your last set of questions, something that really needs to be made is an aggregation service for all the web 2.0 stuff out there. People want an integrated, secure, and trust based work/socializing platform, and my current research interests are geared towards solving this kind of problem. Facebook is trying to do this, but I don't think they have a good mechanism yet for integrating apps.
Hotmail was started because 2 guys didn't want to leave an email trail on their employers' systems.
Ebay was a hobby to help a guy sell his girlfriends stuff.
OTOH, Microsoft, Google, and Amazon were intended to be "deep solutions".
Sounds like you have the passion. No substitute for that.
try the delicious model, build product, refine to user requirement. Then create company around product ~ http://joshua.schachter.org/
If the other part job his intellectual, then it will be much harder, especially if you can't well split activities.
Finally what is really important is how much perseverance, motivation and will you have. The other factor will just influence the amount of difficulty you have to overcome.
However, in vertical markets it only depends on how hard is to develop your version 1.0.
And who are we to tell you if it is possible? Go forth and kick ass!
It's also possible to learn the guitar parttime and play golf parttime.
If you want to be great though, you probably have got to work harder than parttime.
You should have nothing to do with any start-up until you premanently remove those words from your vocabulary.
Seriously.
Anyways, this is part of thinking around the problem.