Of use to you:
http://vmoa.net/VMX12-Service-Manual01.pdf
https://www.vmaxforum.net/threads/new-vmax-owner-faqs-new-members-please-read.21240/
If you post the VIN on the steering head (use XXXXX for the last 5 digits) and the engine case #, we can tell you for what market the bike was built, (if the steering head stickie is still present, that will tell you too) and what year. As it's 34 years old, the engine may have been replaced. We can tell you about the engine year also. A quick check: 1985-'89 bikes have a
5 wire ignition feed/nylon molex plug from the front-left stator area of the engine, for the pick-up coil. The 1990-2007 have a
two-wire ignition feed nylon molex plug, same location. Ignition boxes are different between those.
1985-1992 bikes have smaller (40mm) forks, smaller front brake rotors, and single opposed pistons in each of two front calipers.
I suspect your gas tank may have dried residue from gas left in it. The carbs probably the same. The way to do this (cleaning) with a reasonable expectation of success is to remove the gas tank and the carbs, disassemble them, and for the gas tank, use some type of cleaner. There are many threads on here and youtube about how to accomplish that. If the tank is rusty, Evaporust works but is expensive. I like 6% cleaning vinegar, remove the fuel level sending unit before you soak the tank. A simple block-off plate from steel strap will fill the hole temporarily. Note what can happen to the potmetal sending unit if it's left in the gas tank, instead of using a block-off plate to replace it, when using cleaning vinegar.
Place the tank in a container big-enough to hold the contents of the tank if it should leak. Monitor the results and you should be able to get the tank to a shiny bare metal appearance in a couple days or less.
KBB is a system many use, but you cannot become impatient and 'speed the process,' it won't do what you want it to do.
Electrolysis is another method with its own safety needs.
Look thru the threads on here and choose one, or you may have done one of these before, and will proceed with what's worked for you.
Check the 3 leads from the stator to the left rear passenger footpeg, behind which is the regulator/rectifier. The nylon molex plug for the three wires often deteriorates leading to corrosion, poor conductivity, and a possibility of a short-circuit. Many people solder the wires if the plug is bad. Any one from the front can connect to any one from the back, of the three circuits. Insulate and secure things well.
There is a wire crimp inside the wire harness tape, which will have to be removed to find it, under the seat. It bundles several conductors together. Soldering this connection improves electrical conductivity and delivered voltage in the electrical loom. There are many threads about it.
Either the OEM parts or the K&L carb kits (less $ than OEM) are used to go through the carbs. An ultrasonic cleaner is recommended to do the best job. After removing the carbs (open the cable splice box where the upper cables and the lower cables connect, to disconnect the lower cables from the splice box, for carburetor removal) and the carbs are split into two pairs, front and rear, off come the float bowls. Then the jet block comes off, and the brass jets inside need removal. Use whatever blade screwdriver fits tightest in the brass jet's slot, as you don't want to break-off the brass trying to loosen the jets, there are two per jet block, behind the rubber plugs. Those plugs need to be there for the carburetors to work. Also, the jets should be snugly screwed into the jet block. It doesn't take much torque to fasten them but I have opened a used bike's float bowls for the first time, and found missing round rubber jet block plugs, or unscrewed brass jets floating around and falling out once the rubber plug is removed.
In the gas feed to the two pairs of carbs, there is a molded rubber hose in the shape of a T. On your '89, trying to remove that will probably result in it falling apart, due to age, ozone, UV rays, and hundreds of heat/cool cycles. It's a good idea to have an OEM replacement on hand when you're doing the carb overhaul. At the age of your bike I strongly suggest you replace this. Ever see/have a motorcycle fire?
Out of adjustment enrichener/choke finger followers:
There are several possible causes for this. Getting the enrichener/choke pistons clean and lubricated so they move smoothly usually will fix this.