As you have already guessed, it is very similar to tha tire schreider valve.
Yes, it should have a cap, but the cap isn't ment to really hold much. It is intended to keep the valve clean.
The valve core may not be fully tightened into the housing and could be leaking only because it is slightly loose. It may be leaking because there is a little dirt on the seat of the valve core. Hopefully, it is not leaking because the fuel rail near the valve is cracked.
I don't know if the valve core uses the same tool as a tire valve core. I would try one and see. See if it is loose. If not, remove it and check it for damage or debris. I doubt if the valve core can be interchanged with a tire valve core. You will probably need to obtain one from a dealer. Although I would try to find a fuel valve cap for it, I would try to see if a tire valve cap would fit rather than leaving it bare. That just might be the reason you are having trouble with it now.
