Goku and Vegeta did not have tails and they were training in their God-like Saiyan and then God-like Super Saiyan forms.
Old Kai says about them "These two ain't nothing to laugh at, either. They've mastered energies of a god after all!"
Later Fu says "Now that their power is so perfectly raised, let's see what happens when they're bathed in strong blutz waves!"
they then turn Super Saiyan 4 and Goku says "This power is incredible!" and "This power's like nothing I've ever felt! Guess this is what it's like to be a god, eh?" mind you he has already used and felt Super Saiyan God, God-like Saiyan and God-like Super Saiyan.
So what I get from that is this
1. A tail isn't needed to become a SS4, though once they revert Goku says "Aw man, why do I get the feeling that I won't be pulling that off again any time soon?" hinting that to use the form on your own without needing to be blutz waved every time, you need a tail. (Bulma and Vegeta speculated this in GT)
2.Fu makes it clear that you need a high enough battle power to become a SS4. (Bulma and Vegeta speculated this in GT)
3. Goku and Vegeta were using Super Saiyan, not needing to transform into Great Apes... while in GT they were in base form, and transformed into Great Apes and then Golden Great Apes before becoming Super Saiyan 4.
BTW Super Saiyan 4 Goku here is stronger than Super Saiyan Blue Goku
their convo goes like this
Goku SS4: Heh. Looks like I've got the upper hand.
Goku SSB: Dang it! I'm just...too strong!
Supreme Kai of Time: Is he happy or sad about that? I certainly can't tell.
I used Eternity's quest importer to get the dialogue from Infinite History.