How would an automation tax work? Every time a job is eliminated, add a tax? How much? What if there is further improvement in automation but no further job loses? Does the tax go up? What if it's a new industry and companies jump right to automation and skip jobs? Do they pay the tax? How much?

You could only use it to help fund UBI, unless UBI is significantly less than minimum wage. If the price of buying the robot and running it plus automation tax exceeds what you would spend on employing people at minimum wage, businesses would just keep employing people.

That sounds like a win-win scenario. In cases where robots can do things so efficiently that no human could compete when the minimum wage is a living wage, robots will can do the jobs and anyone who could only have done that job will be OK. In cases where it's cheaper to pay people a living wage than to have robots do it, people can work for a living wage.

That ignores productivity gains. When automation makes things cheaper, it lowers the living wage.

That makes no sense. Just implement a wealth tax because robots increase inequality and make their owners wealthy.