There are people who do contracting for big companies (NetApp, IBM, Microsoft, etc...). How to find such positions? Part-time is as well rarity among engineering jobs for such companies.
* "uncool" work. Stuff noone internally wants to work on.
* time critical - hiring takes time.
* lack of domain expertise - development isn't all equal. Ideally you want people who understand the problem domain.
* quick hit stuff - want something knocked up that'll take 3 to 6 months. Not worth the effort of resource planning internally.
* budgetary - typically contractors in most bigco's (that I know of) don't come from standard headcount budget. Headcount numbers are typically one of the kpi's used to measure growth.
Often times one or more of these reasons conspire together to make a compelling case to go externally.
1. I know that hiring contractors was significantly easier than hiring full-timers. Fewer interviews, less setup time, less coordination with HR or internal recruiters. 2. The other contractors used were supporting legacy software. 1-6 months onsite of full-time work and then limited remote support afterward.
3. If you're paying top dollar and working for you has a large amount of prestige then you want to make sure that your engineers are working on the hard problems. Anything that's not related to that can and should be given to contractors.
To make sure this isn't abused, I think Google only keeps contractors on for 1 year with only a few exceptions
2. Demonstrate usefulness and a value proposition.
3. Discreetly ask for work.
To be even more concise: be an outgoing, valuable individual who is not afraid to ask for work.