Let's go back to the 1 v. 1 first where both players are grasping the ball. If one of them goes to ground such as getting a knee on the ground this is NOT a "tackle". In a tackle the player has to be held as he is on the ground and in this scenario the ball is held, not the player. So, no tackle and no requirement for the man on his feet to release.
However, what about the man off his feet? Does he have to release? I think so but not sure of what law reference if this is not a tackle.
If I understand you correctly ....the answer is 'it depends'.
If in your 1 v 1 scenario, someone was the initial ball carrier...then we are in Law 15 territory so this is important then as to who then 'goes to ground' and the order in which it happens. (If no one was the ball carrier and they were simultaneously grasping for the ball then the ball must have been on the ground and we have Law 14 in play).
For eg, let's call them A v B, where A is the ball carrier. If B has a hold of the ball only, and A 'goes to his knees, and B stays on his feet, then A is technically tackled. B must release the ball (and effectively release player A). Law 15.6 (c) tells us so...
"Players in opposition to the ball carrier who remain on their feet who bring the ball carrier to ground so that the player is tackled must
release the ball and the ball carrier. Those players may then play the ball providing they are on their feet and do so from behind the ball and from directly behind the tackled player or a tackler closest to those players’ goal line.
Sanction: Penalty kick"
Though, if B had gone to ground holding the ball carrier A, just by the ball (the football, not the left or right gonad), but A remains on his feet then I would let him continue to do so. I see that as B trying to affect the tackle and should be given a chance to do so. Equally A could break free and we can play on. (I know B is off his feet, but I don't think he has an obligation to give up the contest that he started while on his feet - I'd let it play out, as I know something else dynamic will soon happen to change the situation. There's no need to blow the whistle IMO).