One was two seperate nipples on the bottom of the faucet. One going to the fresh water tank and the second going to the city water connection. The faucet usually turns for use on city water and you pull and push to use with the fresh water tank.
The other just has a T located somewhere between the fresh water tank and the city water connection with a check valve included that stops the city water from backing up/filling the fresh water tank. The faucet can also be a "crank type" which pumps up an down on fresh water and just pulls down on city water.
JMHO but I'd start at the fresh water tank fill and follow to the fresh water tank. Then look for the output line from the tank to the sink and trace it. Then check from the city water fill to the sink and see whether or not the lines connect or if they do.
As for adding an electric pump, in most all cases it simply means cutting into the line from the fresh water tank and installing the pump and wiring it to a 12 volt source capable of handling apx 5 amp draw.
I have an old school manual t pump. I never use it, the city water connection or the built in tank anymore. I just fill up the 7 gallon aquatainer, set it next to the sink and use that as the faucet. Works great and I never need to clean the tank.
I added an inexpensive electric pump in series with the manual pump line from the water storage tank. It is a lot more convenient to use the onboard water tank by just flipping a switch rather than pumping, but you can still do the manual pumping thing if need be. See pics at Aliner Mods.