Here in NM you would charge the tax then send it to G but first you would be required to register your business with the state and any local G's you are working in.
Of course if you were compensated as an employee, withheld taxes, employer supervision, etc, you would not charge tax but your employer would be required to register.
Someone is responsible for legal compliance during construction. Someone is the GC. If you are merely advising the HO regarding running the project, the HO is the GC and must comply, you are merely his agent. On the other hand, if you are making decisions you might be the GC. So, what does it matter? It will matter if/when someone gets injured. It will matter if/when a neighbor sues. It will matter when G comes looking for taxes. It will matter down the road if/when there is a construction deficiency, real or imagined. It will matter if/when you and the HO have a disagreement that cannot be amicably settled.
These questions are what determine your role and whether you are an employee or an independent contractor and how taxes are handled.