To be honest, it sounds like they're trying to find a way to justify your cost as it sounds like your position is highly specialized.  I would continue putting the least amount of effort in tracking as possible (until direction is provided) and spend any extra energy looking at different jobs.

If you have been with your company longer than this manager, it may be worth talking to someone higher up the chain and mentioning it as an anecdote.  See how they react.  And good luck.

List everything in minute detail - including compiling the list - & including the act of including compiling the list. In the true spirit of 'play stupid fucking games win stupid fucking prizes' piss away as much of your time as possible - with the added bonus of giving them a mountain of tedious bullshit to wade through & asking them questions based on your time accounting so they will have no choice but to wade through it.

They introduced this tired bollocks in a welding/fabrication shop I used to work in - all in the name of correctly pricing the work for customers - which panicked some of the younger welders. Myself & the old fuckers in the shop told them not to worry - do the work & at the end of the shift divide the number of completed works by the number of hours & add in some spurious bollocks - being careful to get as much oil & other workshop shit on the paperwork as possible. Not that anyone is going to go through them anyway - it's all an exercise in throwing a scare into 

>I think I need to line item one hour each week just for this BS micromanagement. Or maybe two? 🤔

Definitely include an entry for it.

You are being managed out. Find another position as soon as possible. Leave with no prior notice; too many rug pulls on offers to risk giving any notice. Employers created the market, you're just operating in it, and looking out for #1 is \*entirely\* professional.

Should I track my task and time usage?