Fuel Pump Issue
 

My fuel pump doesn't work after it is connected to the tank and to the carbs. I have tested the pump, fuel relay and they work/pump just fine when being tested on their own.

Are the carb bowls getting filled, or are they empty? Once the bowls fill and the needle seats, the pump stops (of course). Otherwise, I'd suggest that when installed you're kinking a line somewhere.

Keep in mind that the fuel pump on an f3 does not function until the engine is running.
Could that be what you are experiencing?

Isn't it supposed to prime for a second or two, and then stop till engine is started? Otherwise, you'd never get it running if the carb bowls were dry.

Nope, it doesn't kick on at all until the bike is running. You have to prime the pump, (so to speak) by creating a jumper between 2 female points on it's plug with the key in the on position. It even tells you how to do it in the service manual.

Edit - I am only referring to the way a f3 pump works. I believe other generations may operate differently, but not totally sure about that.

That's insane. So, if the bike runs out of gas and you're not versed on how to do this thing you describe, you're screwed. It can't actually work that way, it makes no sense. Bikes are run dry all the time...intentionally and by mistake. Having to dig into the wiring whenever you ran the bowls dry would be a serious shortcoming, and Honda is simply smarter than that.

Apologies if it seems that I'm being contrary, but there has to be SOME method of getting gas to the card bowls without the engine running - either through some gravitational method through the pump, or by the pump priming when the key is turned or vacuum is sensed from cranking the engine. I do not have the manual for the F3, but may download it to investigate.

Not taking it that you're being contrary, not at all.
The bike will run on gravity. There's some debate on how well or if it should, but it does run on gravity. I've gotten my bike to start from dry like that. It does take a lot more cranking. I may have been unintentionally misleading when I said you "have" to prime the pump. I've just done it that way for so long so as not to potentially drain my battery by cranking it, that I automatically do it when the need arises.
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In the service manual, the process to perform what I described is in section 18, pages 16-17.

If the OP follows those steps, it will tell him if his fuel pump is GTG or not.

The fuel pump electrical supply is controlled by a Solid State Relay (no moving parts).That relay is controlled by signals sent to one bank of the ignition coils. As the coils are energized and turned off in succession, the fuel pump relay is also getting turned on and off. So when you're trying to start the bike, the pump is being provided pulses of electricity. It is enough to make it run, but not much. If your carbs are dry, it can take 15 or 20 seconds of holding the start button before enough fuel has been pumped into the bowls of the carburetors. The method of putting a jumper across the connector is technically used for doing a fuel pump flow test. But it is also a nice way to force the pump to run and fill the bowls.

It's common for people to put a meter on the 2 wires going to the fuel pump expecting to see 12v when they turn the key on. That doesn't happen. Also, even when the engine is running, measuring those same wires won't show a continuous 12v. That's because the relay is providing a "pulsed" supply. You'd need to have a meter that can capture "Peak" voltage. Then you'll see the 12v.