coming from answering the question:
How do I determine the time signature of a song?
I ask you to give some answers for beginners:
-how do you play the first bar? what time is this? 4/4? (we count 12 eighths!)
-which hand is playing which notes?
-how will you play the second and the following bars?
It's common time. I don't remember seeing an edition that writes anything else. It's traditional not to bother writing 3 for the triplets. Perhaps they (very reasonably) felt that it's redundant. It's hard to see what other time signature Bach could have written.
This work was published during Bach's lifetime. Here's the passage from the first edition:
The right hand plays the notes with stems up and the left hand plays the notes with stems down. Much crossing is involved. The second and following bars are treated no differently. The first result I got on YouTube for this gigue was by Sokolov. That video shows the crossing clearly.
Actually, it has been pointed out to me that Sokolov is doing the opposite: playing the eighth notes with the right hand. So is Karl Richter in the guest's answer. I suppose the advice to someone learning this gigue would be to try both ways and go with what feels more natural.
Since a Gigue was a dance, and everybody knew what the dance rhythm was, writing 3's on all the triplets was as pointless as writing a modern "swing" rhythm in triplets rather than equal value notes.
It's also worth mentioning that on the instrument this was written for, a two-manual harpsichord, Solokov's impressive gymnastics on the piano are irrelevant and unnecessary. See
-how do you play the first bar? what time is this? 4/4? (we count 12 eighths!)
replete answers:
It's traditional not to bother writing 3 for the triplets.
I fully agree with the first part of this answer concerning the rhythm performance and note values, also the history of notating. So it's a little kind of nitpicking to defend whether a 12/16 bar is actually a 4/8 with triplets or not as I did in the other question (s. link above) respectively 4/4 with triplets or 12/8 in these Gigue here. But it is certainly not wrong if we discuss the time of a Gigue.
-which hand is playing which notes?
we have 2 videos: Richter and Sokolov. They play both the notes stem up with the left hand. replete as an organist plays them with the right hand and the triplets with the left hand. Obvious both solutions are possible.
When Bach wrote it in purpose to do so he could have written ad libitum.
-how will you play the second and the following bars?
This was the easier part of the question: "Simile" means similar!
in the same way (continuning). With other words: when we study a new piece by Bach - or a similar piece of his period with similar pattern we can also reduce any piece by Bach with a "simile" pattern by notating or memorizing just the chords like Bach did here. I wonder why he didn't so in his prelude in C (WTC 846)
