I would contact a professional tax advisor in Gib, they can answer all your questions, or contact any of the many companies that help people get their residency in Gib.
But in answer to your question, as far as I know.., No you would︀ not pay taxes as long as your company is not registered in Gib, yes you︁ are working from home but you are self employed basically, and whatever money you make︂ it's not made by conduction business in Gib, it's money made outside of Gib, just︃ as if you're running a YouTube channel.
But there are different ways to get your︄ residency in Gib, they all have specific condition, they are all listed online but I︅ would contact a company in Gib, one of the many companies that can help you︆ with your residency and you can explain to them your situation and what you are︇ looking for, there are companies that will not charge you anything just to answer your︈ questions, I've seen a few but it's better that you find your own.
Gib is︉ well known for changing the requirements quite frequently so it's better to talk to someone︊ that can answer your specific questions, you have nothing to lose, but most of the︋ information is online, just takes time to read through all the details.
Hope that helps︌ a little bit...