Jeff,
Here is a response from the pelican parts forum from a guy with an FJ1200 who had similar fuel pump/relay issues...I hope it helps!
On the Yamaha FJ 1200 I had, the fuel pump relay was to turn the pump on only (supply power). The fuel pump itself has a pressure switch built into the pump and would run until pressure shut it off. This is on an 89 FJ1200 and I don't know if a VMax uses the same setup, but I would suspect it does since without the pressure switch the carb float needles will be overwhelmed at any pressure above 1-2 psi.
So, if the fuel pump runs on reserve it may not be getting fuel, and may getting fuel in the "ON" position, pressurizing the line and shutting the pump off.
I would start by insuring that your fuel pump actually pumps fuel in both "res" and "on". Once you have actual fuel flow, stick you're finger over the end and see if the pump shuts off, I believe it should, once again experience with the FJ talking here.
You mention turning the fuel pump "ON" and it sounds like it's been wired through another switch rather than the original design using the ignition switch, is this correct? Is this the original Yamaha fuel pump or is a low pressure fuel pump designed for a car? If it doesn't contain a pressure shut off switch, not just a regulator, then you may be flooding the carbs since it's extremely easy to force fuel past the stock float needles, especially if the pump never shuts off. ( I know this because I tried to replace the expensive Yamaha pump with a 2 psi pump and it doesn't work). Also, the stock pump will flood the carbs if the pressure switch fails in the "on" position.
If none of the above applies, then you've a definite electrical problem somewhere else. I would start by disconnecting systems, running engine and seeing if this has any effect. If one particular system does affect it, then you'll know where to concentrate troubleshooting. Don't forget to disconnect the fuel pump circuit.
If this doesn't work, I would remove the battery, disconnect EVERYTHING from the loom and begin ohming wires, from end point to end point and also, from end point to the frame or any ground. Also, if a single wire runs into a multiple pin connector, make sure that you go from the single wire end point to each of the pins in the connector and insure that you have no shorts wire to wire within the connector. This could indicate either bad connector or shorting of wires in the wire loom.
You'll have to use a wiring diagram since the grounds are often in the connectors and you'll want to make sure that those grounds actually are grounds. Check your battery cables too. You should have very little resistance, if any on individual wires, end point to end point, no more than maybe 50, if that. You should have no resistance to any ground for any ground wire. You should have infinite resistance between wires not on the same circuit and between ground.
A new loom may help or not, depending on the age and abuse it has been subjected to. Often, wires wear through insulation at points where they are tied to the frame, cause by engine vibes and pulling on wires during maintenance or tinkering. Failures are common at stess points (steering head, under the seat, etc) anywhere the loom is exposed to movement, and people poking at it. (People poking things ain't good.)
Don't forget to check your ignition and kill switch, the contacts may be tight enough to run but loose enough to vibrate intermittently. Replace all the fuses with new, old fuses can look peachy and be vibrating causing poor contact.
I would look very closely at your conversion of the coils to coil on plug. They may be arcing to the metal around the plug (head) if they aren't fully insulated, or they may be have a poor contact at the coil connection itself. If possible, try swapping back and see if results change.
One other thing, what fuse is it blowing? That would be helpful.
Hope this gives you some ideas/help.
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