Welcome. You can learn a lot by looking at the factory service manual, of course. Sounds like you've been in it. You should remove the jet blocks, the rubber plugs and the jets behind the rubber plugs. Your pilot jets: probably some or all are plugged. Remove them using a small narrow tight-fitting slot blade screwdriver.
You really should disassemble them and give them a carb soak, I prefer an ultrasonic cleaner.
https://www.vmaxforum.net/threads/new-vmax-owner-faqs-new-members-please-read.21240/
https://dn790009.ca.archive.org/0/i...ice-manual/yamahavmaxvmx12-service-manual.pdf
https://www.vmaxforum.net/threads/ready-for-reassembly.52239/#post-526320
Since you're a student of 1970's/'80's Japanese bikes, you know that CV carbs need to be clean,
really-clean to work well. That goes for all carbs, but a VMax sitting unused for a few months, with 10% ethanol/90% gasoline of 87 octane, is probably going to need carburetor cleaning if the float bowls were not drained, or the engine wasn't run until it quit, w/the gas off.
You're in MI, run the carbs on stock jetting but for the mains, use 150 or 147.5 Mikunis. The bike will run crisper with a bit smaller jets. But the carbs need to be spotless! If they're not clean and all passages unobstructed, you're going to be back on here, asking why isn't it running well?
Look at that thread I posted and use that to set your floats, dry, and you can check them wet according to the carburetor section in the factory service manual.
A 1991 bike will probably have hard, not pliable boots from the airbox to the carb bellmouths, or to the VBoost manifold from the bottom of the carb bodies. You can try boiling them in water to soften them, and quickly putting them in-place, for either the airbox to bellmouth or to the VBoost from the bottom of the carb bodies. Use a bit of water-soluble jelly, like KY or equivalent, to help things slide-together. Make sure that you tighten the clamps properly, all-around.
If you want to make things easy, buy new boots, top and bottom. However, to see if it's worth spending $ on it, I'd attempt getting the engine to run reliably first and then go into upgrades.
A tip on a no-$ way to seat the carbs and the airbox:
See post #2.
Got a carb question
You should feel a 'give' as the carbs seat into the boots, and as the airbox seats into the upper rubber donuts. Look at the casting marks on the carb bodies to ensure they're fully-seated. Take a look at the carb clamps for the rubber boots, and you can see the clamps have 'stops' built into them, to keep you from over-tightening the clamps.
If you want to get the best bite, use a JIS standard 'Japanese-phillips' screwdriver for the X-head fasteners.
