Which of the following construction is the proper or more conventional use of the verb form of the word "trail"? Team A trails (following behind - in scores) team B. Team B trailing (keeping behind - in scores) team A.
Team A trails team B would normally be followed by an amount, e.g. Team A trails team B by ten points. Your second example is not correct, or clear in what you want to say. You are using the present progressive (but incorrectly). Team B is trailing team A is correct and does not require qualifying. Team B is trailing team A by ten points would be correct, or Team A is now trailing team B. (both sentences mean that team B is behind in scores, but the second example suggests a change of position. Team A has been trailing team B the whole game. This example uses the present perfect to express a time duration. I would suggest that the use of the present progressive is better, unless you're a sports commentator and don't want to waste time saying longer sentences.
Team A trails Team B is good.
In the second one using trail to mean keeping behind doesn't seem right at all
Team B leads Team A would be better if you want to use them in that order.
I think I see where the confusion might come from.
It's normal to say Jim trails a bag along to mean Jim is pulling a bag that is behind him but that's a different definition of the verb trail. See Oxford Dictionaries (verb defn. 1 & 4)