Well, yes we do know based on Scripture....ALL the disciples fled Him.
Mark records this as does John.
And they all forsook him, and fled Mark 14:50-52
Behold, the hour cometh, yea, is now come, that ye shall be scattered, every man to his own, and shall leave me alone: and yet I am not alone, because the Father is with me. John 16:32
--- possibly he just went to get Jesus' mother
possible but doubtful considering the hour.
--- but either way, he must have returned promptly, because we know he was there with Mary, at the Lord's crucifixion to the end. At that point, the Church Loyal was indeed very small at the foot of the Cross: very small.
This is correct. John was at the Cross.
As I said....some were corrections and some were clarifications.
I'm entitled to that opinion-- just a supposal--- because it does not contradict the known facts, and the text itself does not go into further detail. John does seem to have been closer to Jesus than the others: being known as the "beloved" one.