I’ve just done a few months as a remote worker in Taiwan for a Canadian company myself. I returned just a couple of months ago to Canada. Here was my experience:
On the Taiwan side there was no issue. I wasn’t technically working in the legal sense in Taiwan since I’m a Canadian employee working for a Canadian employer being paid in Canada. So I entered on a visitor visa, so there were no taxes or paperwork involved.
The Canadian side was more difficult. It certainly did matter to my employer because if I was to move there, I would be technically working there and then there would be a whole slew of legal and administrative requirements that they would need to comply with to support my employment in Taiwan.
My solution was to find out how long I could exit Canada (and my province) without losing residency status – specifically for taxation and healthcare – and visit Taiwan for a lesser period. The argument goes, “if I leave for 2 week then the company is cool and the government’s cool. What if I leave for 3 weeks, or 3 months? At what point would my status change? Let me be gone for up to that time”. My company agreed and we drafted up a memorandum of understanding that I would return to Canada before the agreed upon date (I’m grateful for my employer in humouring me on this. They consulted external legal advice and took a chance that I wasn’t taking off forever). I think it helped that my job used to have a fair bit of travel already, back when we did that kind of thing.
You wrote that you’re thinking of just a few months. So I’d recommend the same: lookup the residency requirements in New York (or rather when they would expire if you left, especially for taxation) for your situation and approach your company likewise to propose your plan and see if they have a policy in place for this already. It would go a long way if you show you did your research first and propose a guaranteed return date which would free them of some of the anxiety of HR or legal consequences of the unknown.
And don’t forget to look into healthcare options for Taiwan: paying into Taiwan’s system if you can, private insurance, or if existing coverage from your employer covers you internationally and for how long.