How to share responsibility for part of my advisor's project, which I did not create and I am insecure about?
One question additional question I've got, you state you're not funded under the funded proposal. Does that mean you came to your advisors group with your own funding or are you being paid by the department to TA or something related?

I ask this because the above two funding situations for a PhD student means the advisor is free to spend what would otherwise have been your salary on materials, equipment, or other personnel. But your efforts can still be attributed to the project. So unless your source of funding is conditional on publishing, I wouldn't worry about how the various things you're working on are funded.

That said, if you find your current efforts interesting and exciting, stick with it and try to align your research plan with it. As a first year PhD student, you have the time to spend developing an apparatus(you've got 3 or so years extra over postdocs or masters students). And if you do get the apparatus setup and working, that sets you up as the person in charge of the equipment, paving the way for collaborations.

Though I would advise you to do your best and layout a timeline for your advisor, and make him aware of your timeline. If he wants faster results you can always suggest the intermediate steps such as your hunch(nothing beats experimental results), or ask for assistance from the more senior members in your group.