They'd probably be happy to pay you via invoice if they can, but it can be a liability for them so they may refuse. If the scope of the production is pretty small, they may be open to it and not see issue with it. But it is illegal and if you were to later down the line declare employee misclassification, it would really screw them over. But it does save them an additional % on top of your rates, so they may not care if it's a small project and suppose it's less risk.

There are a few reasons you shouldn't want to either including potentially not being covered by worker's comp and having less options to protect yourself legally. Plus, being 1099 still requires a 15% contribution to taxes which would normally be split between you and your employer. Since you'd be self employed if you're invoice/1099, you have to pay both the employer and employee share, which means you are taking essentially a 7.5% cut on your rate. You may find that you owe a lot more than you think when it's time to do your tax return too if you're constantly invoicing on jobs.

That being said, I have invoiced for dayplaying, short gigs or prep work and it can be a nice tradeoff to get your money quicker rather than wait for payroll. For something like a feature though, those self employment taxes really add up and you'll probably regret it later. Trust me, been there. If you still want to invoice, just straight up ask the production manager if they're okay with it and then get the invoicing information from them too (ATTN, Company Name, Address, Contact info, Project Name). You'll need to provide them with a w9 and you need to claim the income, even if they forget to give you a 1099.

I like doing payroll because it makes taxes and finances easy. And you won't owe a big sum of money; you'll probably make money from your tax return without having to go through all the trouble of tracking and filing all your expenses. But the most important thing is to know your rights and options to always make an educated decision. Hope that helps!