No, it's not shorting if it's taped. If it was shorting, you'd see clear signs of melting/burning. A dead-short across the battery would result in unambiguous evidence of same.
I'm making a screwed-up squinty-eye face on the "did run the tank empty" comment
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I'm thinking your pump is bad. Just because it pumps doesn't mean it's good. You need to find yourself a clamp-on Ammeter and see how many Amps it's pulling while it's running. Given that you replace the fuse and get a few minutes of driving before it pops again, I'd suggest you leave the meter on with the engine running and see if the current changes over time. A common failure mode in an overheated electric motor is "shorted windings". The magnet wire coil is only insulated with a coating of enamel (or Kapton or something similar that's really thin so you can get more turns of wire around the armature, you're not losing space to insulation). If it gets hot enough, it carbonizes or melts in spots and those spots become susceptible to short circuits. The motor, even immersed in gas, will get hotter the longer it runs. As it does, things start to move mechanically due to thermal expansion. A motor that starts just fine when its cool can suddenly start to draw more current once it warms up, if the winding insulation is damaged. The short circuit that causes the current to go up doesn't happen until heat makes things move enough to bring the shorted sections of the windings together.
You won't need to cut any holes in the car to measure the current draw of the pump. So do that before you decide the pump is bad and go through all the effort to gain access to it.
