What counts as "working" in the US?

I will be travelling to the USA and may be spending up to six months there. It's also very possible that I will marry a US citizen and apply for permanent residency (not a sham marriage - a real one.) I am an Irish citizen, living and working in the UK, for a UK-based employer, paying PAYE, NI etc. as normal.

My employer is keen to retain me for some time, maybe indefinitely, because 95% of my job is online, so I can work from anywhere. If I was to keep working at my current job, and continued to get paid into my UK bank account, paying UK taxes as normal, would I be in breach of US tourist visa regulations?

Bit of a grey area so technically no unless you declare it. Keep quiet and enjoy your 6 months