I start with a few internal questions.
1.) What are the conditions? With me, probably a Caribbean or southern Florida area dive, excellent viz., minimal current. There's likely a guide leading the group.
2.) Why am I buddy diving? Often I'm just diving with the group, so it's really not (in which case I view the leader as a GPS-like navigation aid and may helicopter to conserve air and make him easy to follow). Sometimes someone invites me on a buddy dive apart from what the group is doing (happened on a live-aboard trip out of Belize), or the solo dive I might've been going to do (as happened in California). If that's the case, the other diver is likely more seasoned and capable at navigation, so I follow him, close but back a little. Trying to pace someone 'shoulder to shoulder' sounds impractical and aggravating to me...I don't do that on land, either (my wife thinks it's an only child thing; I don't know).
3.) What do I expect from the buddy? Usually, a GPS-style navigation device. We may point out to each other things we find, but that's about it. I don't expect him to 'baby sit' me, constantly monitoring if I get into trouble or have a serious medical event. I can grunt loudly to get attention; if I didn't think that was good enough I could bring a tank banger. I drive solo on the Interstate without a 'buddy,' and I don't expect one to constantly monitor me on a dive. If I'm back a bit and he's leading, it's my responsibility to keep up (assuming he's not going fast). We glance at each other intermittently. As for checking remaining gas, I'm likely a little worse on air than the other guy, so when I'm at half-tank or so, I'll get his attention and let him know. I don't expect him to ask me.
4.) What does the buddy expect from me? The kind of diver apt to invite me along probably doesn't expect me to constantly him, or feel the need to do it to me, but I try to be reasonable and adapt.
There's a situation I've run into, albeit seldom, when the boat crew puts me with a buddy. I don't like having an assigned instabuddy, but if necessary... We talk before the dive and I try to get a sense of whether this is a new diver, a stickler for formal adherence, etc..., and work with that.
Real world example from several years ago. Diving in Key Largo, I get paired with an instabuddy. Okay, guide-led group dive (yet I'm assigned a specific buddy...), I glance at him once in awhile, dive goes okay, end of dive we surface behind the boat, haul ourselves in on the 'granny line' (or whatever you call it), get out. Back on boat, a staff (politely) fusses at me because I didn't stay with that guy at the very end and got out without him (the guy complained). They paired me with another guy next dive, I think one of their regulars. End of that dive, I'm looking around on the line, guy's nowhere to be found, I finally get out...new buddy had already gotten out and back onboard ahead of me. Which is fine with me!
My point is, with instabuddies, there are a range of real world expectations, often unspoken, and on-boat spontaneous encounters don't lend themselves to the more 'stickler' type dictating to the other diver 'Hey, this how it is going to be.' A little reasonable respect and accommodation from both goes a long way.
Change the situation to low viz., high current or other complicating factors and that's another story. My view on buddy diving in good conditions by intermediate and higher level divers is politically incorrect, but I suspect real-world prevalent in the Caribbean region.