Sursula already answered the vacation part of it, so I'm not covering this. The only small addendum I have to that is that, of course, taking leave from one place doesn't mean you are automatically free from your obligations in the other - quite the opposite, what I see my colleagues with dual appointments often doing is using the vacation at their main place of work to fulfill their teaching obligations at the other.
But practically it's hard to get part-time positions. If someone manages to do it then how is it possible?
Part-time positions at universities aren't all that unusual per se, but maybe not with the percentages you have in mind. Generally speaking, when we hire we are looking for either a full-time staffer or somebody covering one specific need (oftentimes a teacher for one specific course). For the former, a 70% appointment would probably be hard to negotiate, and for the latter 30% is sort of too much. So the much more common arrangement is that people have a 100% employment at one place, and a small (10% - 20%) teaching or research assignment somewhere else. Typically, obligations with the secondary place of work are negotiated in a way that they can be done in blocks and do not require much ongoing presence (e.g., a seminar that can be done in block in three weeks, or a research project that can be done primarily remotely).
You can of course always apply for a full-time position and attempt to negotiate it down to 70% or 80%. I would not expect much enthusiasm for this plan, but depending on their specific needs (and how desperately they want to hire specifically you) it may work. Smaller part-time positions are usually found through your network - I would say, if you are an active researcher with decent standing in your local community, it's not particularly difficult to find a university that is willing to give you a small adjunct position (often in exchange for teaching a course per year) - but, again, being an adjunct teacher for 30% or 40% of the time may be more problematic, as at this point this starts to look too much like a normal professorship and may need to go through the usual formal hiring channels.