Lands don't have a subtype just because they can produce mana of the corresponding color. Game Trail itself is neither a Mountain nor a Forest, even though it produces red and green mana, so you can't reveal one to satisfy the ability of another.

If an effect instructs you to put Game Trail onto the battlefield tapped, it will still enter the battlefield tapped even if you reveal a land card from your hand.

You may reveal any land card with either or both of the appropriate subtypes. It doesn't have to be a basic land. For example, you could reveal Canopy Vista from the Battle for Zendikar set to satisfy the ability of Game Trail.

If a Mountain or Forest is entering the battlefield from your hand at the same time as Game Trail, you may reveal the other land to have Game Trail enter untapped.