fuel tank equalizer

That's a cross over valve. Most people leave that open so the tanks go down equally. If you have problems with the fuel in one tank you may close off that tank, but more often it's used when running long distance with a beam sea so that you can keep more weight on the side the seas are coming from for stability and a smoother ride. Although I've seen them with a pump they are usually gravity fed so the motors can be running or not. That label and the fact that it is higher than the tanks is a bit confusing though. Yours may be operated by a pump.
P.S. That's a great thing to have. I once transported a boat to the yard. It had just about enough fuel to make the trip until one transmission blew leaving the other to do all the work. It was frustrating as I watched that fuel gauge drop to zero while I had fuel in the other tank that I couldn't access. I'd have been willing to suck diesel if I even had a garden hose on board, but no such luck.

it should be kept closed unless you have a good reason to need it open, like needing to access the fuel in the other tank.

if it's left open and the boat starts listing (for any reason) fuel will flow to the lower side and may not return when the list is correct. ex... if you're launching a tender, the boat may list while launching. during that time, fuel will flow across if the valve is open...

if the valve is higher than the tank then you probably have a pump somewhere, trace the hose from the valve to each tank.

Fuel Tanks crossover

I would suspect that you have one fuelling point and that valve may be to allow filling of the other tank when the first one is full, as Pascal says, trace out all fuel lines coming and going !!