From someone who's sort-of worked like this for a while - sure, the time off between contracts is nice, but the contracts themselves are much more intense than regular full-time work - partly because you're pretty much always on-boarding and catching up, and partly because client's management does not care about contractors and will treat you worse than full time employees. Just something to keep in mind.
That is the job of a recruiter. Find one that specialises in your technology/sector and contract work.
10X Management does this (they represent me). I know they aren’t the only agency representing software professionals, but I don’t have experience with any others. Some recruiters and placement agencies work this way.
Finding customers and getting contracts can take a lot of (unpaid) time for freelancers. I look for long-term relationships rather than churning short-term projects. You can still take time off if you don’t leave your customers hanging.