Having a car sit for only a week and have the carb be dry sounds more like a leakage problem. I know with a Holley carb if the power valve begins to leak it will eventually drain the bowl where the valve is. If you are going to install an electriced powered booster fuel pump, then just be sure that you get one for a carb and not EFI. An inline pressure regulator might be a good idea to keep the fuel pressure on or about 5 psi.
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