The fuel pump itself is not rebuildable though it's possible the o-rings where the fuel lines connect coul be bad. More likely however is the anti-drainback valve inside the fuel pressure regulator that sits atop the fuel pump is leaking. When it leaks, it allows all the fuel that is supposed to remain in the fuel rail next to the fuel injectors to leak back down to the fuel tank. The long start is how long it takes for the fuel pump to get the fuel back up to the fuel rail/fuel injectors.
You can often find the TJ's fuel pressure regulator sold separately on eBay. At the dealer, you can only buy it as part of the fuel pump which is a lot more $$$.