How can I create a giveaway for BASE game what has been removed from the giveaway list?

You can sadly not gift Euro Truck Simulator 2, as it has previously been given out for free.

You can post a status to your friends on Steam, and have them leave a comment, if they want the game. Then, you can use a website like Random.org to draw a number to determine the winner.

you can gift it to me lol

What should I do?

I've seen some users use a method :

They choose a game from the list and then say in GA description that it's actually another game.

I don't suggest it.

there is a thread floating around where you can post these kind of keys.

You can post it here if you want to give it: http://www.steamgifts.com/discussion/MYeOi/orphan-keys-drop-thread

the best you can do right now is hit
http://steamcommunity.com/id/[yourusername]/friendsthatplay/227300
and see if any of your friends is under the "Friends who want Euro Truck Simulator 2 " section
otherwise you can open your friends list and manually sort out the "All friends who own this" list and give it to one of the remaining friends.
[just tried putting a different name in the above link to check if someone else's friends might want something but it just bounces back to the version for your profile]

I've seen two methods. One is to do a GA on the forum. I did that once early on. You can use a random number generator like Random.org to choose a winner.

I've also seen people do linked GAs--list a game and then say in the description that the winner will also get something else. It needs to be ALSO, not INSTEAD OF per the rules. Also, if you want to make sure you don't give it to somebody who actually just wanted the main game, you can make that a group or whitelist GA to avoid a lot of traffic that won't read the description.