Nooooo! There are no costs and effects in Summons. They're Summons, just that. It may be convenient to
compare effects and Summons, but they actually are different, so don't call the first part of Summons costs.
Test Tiger
Effect Monster (Beast / EARTH / 3 Stars / ATK 600 / DEF 300)
If you control a "Gladiator Beast" monster, you can Special Summon this card. You can Tribute this card to return 1 "Gladiator Beast" monster you control to the Deck, and then Special Summon 1 "Gladiator Beast" from your Deck. The Special Summoned monster is treated as if it was Special Summoned by the effect of a "Gladiator Beast".
Now, Test Tiger wants to do something to a "Gladiator Beast" monster here. The problem is, face-down cards on the field are
only "face-down card"s - they have no names. You can't check the name until you do something to it (other than target it, of course), such as Tributing it or sending it to the Deck or whatever. Basically, if you would target a face-down monster, you'd have to trust that it's a "Gladiator Beast" monster because there's no way to check until resolution. If it turned out
not to be a "Gladiator Beast" monster after all, it's an illegal activation, but there's been a chance to chain to the effect already (which may have happened multiple times). That means you'd have to rewind all those chained effects, and that's a huge nuisance. In other words, it's not allowed, therefore face-down monsters cannot be targeted by Test Tiger.
Summons (such as Contact Summons), however, Tribute the monsters during the first part of the Summon (the "cost" of it if you must use incorrect terminology), so you
can check what monster it is at the start of the Summon. If it turns out to be the wrong monster, there's practically nothing to rewind, so it's allowed.
In short, if you need a specific monster for something, you can use one that's face-down
as long as you do something to it
during the cost or the first part of the Summon (which is always the case for Summons). If you only need to
target that specific monster during the cost (or do nothing about it), then it can't be face-down.
So after nearly a month, it seems I
could answer the question after all.