My perspective, most of which was raised by others.
Designate a leader. You can switch off during the dive, but there must be absolutely no question about who is leading and who is following at all times during the dive.
Relative positioning is critical, In general a side by side positioning is best, especially with low vis. The leader can be a few feet ahead, but it is so much easier, if he doesn't have to constantly be looking back. It is also essential that the two buddies are at the same depth.
With regard to relative position, you MUST STAY in the same relative position. This is where a lot of separations start. If your buddy is on your left, make sure he stays there. If you two want to change relative positions, say on the way back, no problem, but make it clear and work slowly when you re-position and then confirm frequently that the new relative position has been established and is being maintained.
When you are the leader, you need to communicate changes in trajectory or path. If you are following a linear structure, then keep following it and if you decide to go over it or turn away from it, then the leader should signal the change in course, do it slowly and immediately confirm that the follower is still following. This is super important. Don't do ANYTHING unusual or unexpected without communicating and confirming that the altered course/objective has been accepted and understood by the follower.
If/when you get separated, agree to both return to the last place you saw each other. Same as you do when you are shopping at the mall. If both buddies are moving slowly and are attentive, this should be a distance of 15 or 30 feet max and a time of 60 seconds.
Using lights is a big help in many situations.
Agree on what happens if you don't find you buddy in specified time.
If you follow these ideas and the vis is like 5-10 feet and there are no terrible surges or currents, and both people are motivated to maintain the team, you should have infrequent and short separations. A good buddy team will learn to do most all of this instinctively.
If you both are nervous about buddy separation, then maintain a VERY close shoulder to shoulder position. It is no big deal if you bump shoulders once in a while or kick your buddy's fin. This is much less objectionable and burdensome than having both divers have one hand fully occupied by holding a rope. As you have heard, clipping off to each other is unwise.
As you get better at it, your shoulder to shoulder positioning can widen somewhat, but the concepts of leader/follower, not changing relative positions without notification and not changing course without acknowledgement, will continue to be essential.