Nanny or daycare options in Taichung?

My son (22 months, non Taiwanese citizen) will be in Taichung, Day for about 1.5 months. We’re trying to look for regular half day child care while we sort out my grandfather’s stuff (he has dementia, is going blind) so a lot of our visit is being spent working on figuring out elder care as well as shuttling him in/out of hospitals. Anyone know of any childcare options for non-citizens? Would prefer exposure to other children, etc. We contacted some regular daycares and there are no openings. Anyone have any thoughts? My parents haven’t lived in Taiwan for about 3 decades and we don’t have anyone else with kids we regularly talk to.